Suppose a population of honey bees in Ephraim, UT has an initial population of 3600 and 12 years later the population reaches 25000. Use an explicit exponential model to find the rate of growth and common ratio for the honey bee population.

Express the rate of growth as a percentage. Round to the nearest tenth.

r=%

Express the common ratio as a decimal. Round to the nearest thousandth.

1+r =_

Answers

Answer 1

1) The rate of growth for the honey bee population is approximately 10.1%, rounded to the nearest tenth.

2) The common ratio is approximately 1.101, rounded to the nearest thousandth.

We can use the formula for an explicit exponential model:

N = N0 × (1 + r)^t

where N0 is the initial population, r is the rate of growth (expressed as a decimal), t is the time elapsed (in years), and N is the final population.

We can use the given information to write two equations:

N0 = 3600

N = 25000

t = 12

Substituting these values into the formula, we get:

25000 = 3600 × (1 + r)^12

Solving for (1 + r), we get:

(1 + r)^12 = 25000/3600

(1 + r) = (25000/3600)^(1/12)

(1 + r) ≈ 1.101

r ≈ (1.101 - 1) × 100% ≈ 10.1%

Therefore, the rate of growth for the honey bee population is approximately 10.1%, rounded to the nearest tenth.

2) The common ratio is 1 + r, so

1 + r ≈ 1.101

Rounding to the nearest thousandth, we get:

1 + r ≈ 1.101

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Related Questions

What is the conversion of 2000 pounds to dollars ?

Answers

The conversion of 2000 pound sterling to dollars is 2,740 US dollars.

The conversion of 2000 pounds sterling to dollars depends on the current exchange rate between the two currencies.

The exchange rate was approximately 1.37 US dollars per 1 British pound.

Using this exchange rate, we can convert 2000 pounds sterling to US dollars as follows:

2000 pounds * 1.37 dollars/pound = 2,740 US dollars

Therefore, 2000 pounds sterling is equivalent to approximately 2,740 US dollars using the exchange rate mentioned above. However, please note that exchange rates can fluctuate over time, so the exact conversion may be different depending on the current exchange rate.

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Correct Question :

What is the conversion of 2000 pound sterling to dollars ?

Find the orthogonal trajectories for the family of curves. (enter your solution in the form f(x, y) = c or y = f(x, c) where c is a needed constant. ) y = ce5x

Answers

Refer to the attached image.

a box plot is a graphical representation of data that is based on a histogram. z-scores. a five number summary. the empirical rule.

Answers

A box plot is a graphical representation of data that is based on (c) a five number summary

How to complete the statement

From the question, we have the following parameters that can be used in our computation:

Statement: a box plot is a graphical representation of data that is based on__

A box plot (also called a box-and-whisker plot) is a way to display the distribution of a dataset.

It shows the median, quartiles, minimum, and maximum values of the data.

These items are referred to as the five number summary

Answers

10m for the 1st floor. 7.32m for the 2nd floor.

What is the Trigonometry?

Trigonometry is a branch of mathematics concerned with relationships between angles and ratios of lengths.

Let the point where the man is standing on window be A.

Let the point where the dustbin is there be B.

Let the foot of the building be C.

So, according to the given details,

CB = 10m.

angle (ABC)= 45 degrees.

Let the point of the 2nd floor be P.

We must understand what the angle of depression is: It is the angle measured below the horizontal level.

In triangles ABC and PBC, we use trigonometric ratios as follows:

[tex]tan(45) = AC/BC\\\\AC = BC = 10cm.\\tan(60) = CP/BC\\\\CP = BC\sqrt[2]{3}\\CP = 10\sqrt[2]{3}\\ CP = 17.32m. \\\\2ndfloorheight = CP - AC = 7.32m[/tex]

Hence, 10m for the 1st floor. 7.32m for the 2nd floor.

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What is the inverse of the function f(x) = (x-2)^4?

Answers

Answer:

In order for f

to have an inverse, it must be a bijection. That is, it must be an injection and a surjection. So we must restrict the domain and codomain appropriately. It is standard that the square root operation returns positive values, so we use that as the basis for our restriction.

all rational functions have vertical asymptotes. (True or False)

Answers

True. Rational functions are defined as the division of two polynomials. These functions are limited in their scope and, as a result, have specific properties. One such property is the existence of vertical asymptotes.

Vertical asymptotes occur when the denominator of a rational function approaches zero, resulting in a discontinuity in the graph of the function, or a point at which the function can approach but never reach. This creates a divide in the graph, resulting in two halves with a vertical line at the point where the denominator equals zero. This vertical line is the vertical asymptote of the rational function. In conclusion, all rational functions have vertical asymptotes due to their limited scope and specific properties.

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A number z divided by 2 is at least -6.

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A number z divided by 2 is at least -6 is expressed as z ÷ 2 = ≥ -6

What is division?

One of the fundamental arithmetic operations in mathematics is the division, which is the process of dividing a group of items into equal parts. Every day, we might use the division technique in various situations.

One of the four fundamental arithmetic operations, or how numbers are combined to create new numbers, is division. The additional operations are multiplication, addition, and subtraction.

On a fundamental level, counting the instances in which one number is contained within another is one interpretation of the division of two natural numbers. 7 It's not necessary for this number to be an integer.

The expression to represent this problem is:

z ÷ 2 = ≥ -6

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Austin bought some belts online for $26. He used a coupon code to get a 40% discount. The website also applied a 10% processing fee to the price after the discount. How much was the discount, in dollars and cents?

Answers

Answer: the discount in dollars and cents was $10.40.

Step-by-step explanation: Austin bought some belts online for $26. With a 40% discount, the price of the belts is reduced by:

Discount = 40% x $26 = $10.40

So the new price after the discount is:

$26 - $10.40 = $15.60

Then a 10% processing fee is applied to the discounted price of $15.60, so the final price paid by Austin is:

Final price = $15.60 + 10% x $15.60 = $17.16

Therefore, the discount in dollars and cents was $10.40.

ANSWER : Austin got discount of 8.84 $ and 34% of price of belt.

EXPLANATION

Price of belts is $26.

Price of belts after discount of 40% = $15.6

(60% of 26 is 15.6)

Price of belt after processing fee of 10% = 17.16

(110% of 15.6 is 17.16)

Final discount in $ = Price of belt - Price of belt after processing fee

26-17.16=8.84

Final discount in % = (8.84*100)/26 =34%

how to convert ml to quarts

Answers

Answer:

1 milliliter = 0.00105669 liquid quart

Step-by-step explanation:

What are units?

A unit can be used for measurement, and is commonly found in mathematics to describe length, size, etc.

Converting these units:

1 milliliter = 0.00105669 liquid quart1 quart = 946.353 ml

Therefore, for every 1 milliliter it is equivalent to 0.00105669 liquid quart.

solve the quadratic equation 3x^-75=0

Answers

Answer:

Below

Step-by-step explanation:

Since it is a QUADRATIC it should be

3x^2 - 75 = 0 divide through by 3 to get

x^2 - 25 = 0 then

x^2 = 25

x = ±5

The Tabletop Games club, a student-led campus group, hosted a virtual concert last week to raise awareness about their club and bring community members together. They sold full-price tickets for$7. 00, tickets for senior citizens were $5. 25and student tickets cost $5. 50. After the concert, they counted up the totals. There were a total of 215 tickets sold, and ticket sales brought in $1,214. 0. It was noted that there were 3 times as many senior citizen tickets sold as there were full-price tickets. Write and solve a linear system to determine how many of each type of ticket were sold. There were _____full-price tickets. There were ____senior citizen tickets. There were ____student tickets

Answers

There were 42 full-price tickets sold, 126 senior citizen tickets sold, and 47 student tickets sold.

Let's define the variables:

Let's call the number of full-price tickets sold "f".

Let's call the number of senior citizen tickets sold "s".

Let's call the number of student tickets sold "t".

From the problem statement, we know:

The total number of tickets sold is 215: f + s + t = 215

The total revenue from ticket sales is $1,214.00: 7f + 5.25s + 5.50t = 1214

The number of senior citizen tickets sold is 3 times the number of full-price tickets sold: s = 3f

We can use the third equation to substitute "3f" for "s" in the first two equations, and simplify:

f + 3f + t = 215 -> 4f + t = 215

7f + 15.75f + 5.50t = 1214 -> 22.75f + 5.50t = 1214

Now we have two equations with two variables, which we can solve using any method of our choice. For simplicity, we will use the substitution method:

From the first equation, we can isolate "t":

t = 215 - 4f

We can substitute this expression for "t" in the second equation, and solve for "f":

22.75f + 5.50(215 - 4f) = 1214

22.75f + 1182.5 - 22f = 1214

0.75f = 31.5

f = 42

So, there were 42 full-price tickets sold. We can use the third equation to find the number of senior citizen tickets sold:

s = 3f = 3(42) = 126

Finally, we can use the first equation to find the number of student tickets sold:

f + s + t = 215 -> 42 + 126 + t = 215 -> t = 215 - 42 - 126 = 47

Therefore, there were 42 full-price tickets sold, 126 senior citizen tickets sold, and 47 student tickets sold.

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function w gives the weight of a cat, in kilograms, when it is m months old, which statement represents the meaning of the equation w(7) = 4 in this situation?

Answers

Using the given equation, The weight of a cat when it is 7 months old is 4 kilograms.

Which equation is this?

Equations describe physical processes and the relationship between different physical quantities. Equations are mathematical and physical statements. Physical quantities are presented using simple variables, and after that, a personal variable, such as your energy, may be indicated.

An equation can be defined in numerous ways. Algebraically speaking, an equation is a statement that shows the equality of two mathematical expressions. For instance, the two equations 3x + 5 and 14, which are separated by the 'equal' sign, make up the equation 3x + 5 = 14. Algebraic equations in mathematics frequently have one or more variables.

In this situation, the statement "w(7) = 4" represents that a cat that is 7 months old weighs 4 kilograms.

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Find the volume of the solid generated by revolving the region in the first quadrant bounded by the coordinate axes, the curve y = €* and the line * = 8 about the line x = 8.

Answers

The volume of the solid generated by revolving the region in the first quadrant bounded by the coordinate axes, the curve y = e^-x and the line x = 8 about the line x = 8 is approximately 1483.6 cubic units.

To find the volume of the solid generated by revolving the region in the first quadrant bounded by the coordinate axes, the curve y = e^-x and the line x = 8 about the line x = 8, we can use the method of cylindrical shells.

To find the volume of the solid, we need to integrate the area of each cylindrical shell over the height of the solid. Let r be the radius of a cylindrical shell at height y, and let h be the thickness of the shell. Then the volume of the shell is given by:

dV = 2πrh × h

where the factor of 2 comes from the fact that there are two cylindrical shells (one on either side of the line x = 8).

We can express r and h in terms of y:

r = 8 - y

h = e^8 - e^-x

Substituting these expressions into the formula for dV and integrating from y = 0 to y = 1, we get,

V = ∫(0 to 1) 2π(8 - y)(e^8 - e^-x) dy

= 2π ∫(0 to 1) (8e^8 - 8e^-x - ye^8 + ye^-x) dy

= 2π [8e^8 - 8e^-1 - (1/2)e^8 + (1/2)e^-1]

= 2π [15e^8 - 4e^-1]

≈ 1483.6 cubic units

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The given question is incomplete, the complete question is:

Find the volume of the solid generated by revolving the region in the first quadrant bounded by the coordinate axes, the curve y = e^-x and the line x = 8 about the line x = 8.

What is derivative of e 2x ?

Answers

The derivative of e²ˣ is 2e²ˣ.

A derivative of any function is the rate of change that will be made on the function if its independent variable changes by a small amount.

Now a function can also have another function in it. Then if we need to find the derivative of that function we need to use the chain rule. This states that for any variable x, if there is a function

f(g(x)) then derivative of f(g(x) will be f'(g(x))⋅g'(x)

this means that we need to first hold the function in it constant and then multiply the function's derivative with respect to x.

Here f(g(x)) = e²ˣ where g(x) is 2x

Now we will first hold 2x as one variable. We know that d/x of eˣ is eˣ

Hence we get

e²ˣ

Now we will differentiate 2x. The derivative of 2x is 2

Hence we get the derivative as

2e²ˣ

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(2x2 x 10) x (10^58 x 10^-27)

Answers

The simplified expression is [tex]4.0 \times 10^{32}[/tex]

The term "algebraic expression" means what?

A mathematical statement without an equals sign that contains variables, constants, and mathematical operations is known as an algebraic expression. Algebra and other branches of mathematics both employ algebraic expressions to represent mathematical connections.

Simple algebraic expressions include x + 2, which consists of the addition operation, the constant (2), and the variable x. Several variables, constants, and operations can be found in more complicated algebraic formulas, like 2x2 + 3xy - 4.

Whereas constants are fixed values that never change, variables in algebraic expressions indicate unknowable values that can vary or change. Variables and constants are combined using mathematical operations including addition, subtraction, multiplication, and division.

In several academic disciplines, such as physics, chemistry, economics, and engineering, algebraic expressions are employed to solve issues. Moreover, they are used to manipulate and simplify mathematical formulas and equations as well as to mimic actual life circumstances.

By combining like terms, or terms with the same variable raised to the same power, algebraic expressions can be made simpler. For instance, the like words 3x and 2x in the equation 3x + 2x + 5 can be combined to create 5x, resulting in the abbreviated expression 5x + 5.

[tex]2\times 2 \times 10 = 20\times 2[/tex]

Next, we can use the rule that when we multiply two numbers with the same base, we add their exponents. Therefore:

[tex]10^{58} \times 10^{-27} = 10^{(58-27)} = 10^{31}[/tex]

Putting it all together:

[tex](2\times 2 \times 10) \times (10^{58} \times 10^{-27}) = 20\times 2 \times 10^{31} = 40\times 10^{31} = 4.0 x 10^32[/tex]

Therefore, the simplified expression is [tex]4.0 \times 10^{32}[/tex]

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Find the area of the composite figure.

Answers

The area of the composite figure is equal to 52 square units

How to calculate for the area of the figure

The composite figure can be observed to be made up of two congruent triangles, and a parallelogram, so we shall calculate for the areas of the three figures and then add the result to get the total area of the composite figure as follows:

area of the one congruent triangles = 1/2 × 8 units × 4 units

area of the one congruent triangles = 16 square units

area of the parallelogram = 5 units × 4 units

area of the parallelogram = 20 square units

total area of the composite figure = 16 square units+ 16 square units + 20 square units

total area of the composite figure = 52 square units

Therefore, the area of the composite figure is equal to 52 square units

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help me for 30 points!!.

Answers

Answer:

d!!

Step-by-step explanation:

When you create a dot plot, you do which of these operations? Select all that apply.
Multiple select question.
Add a vertical axis showing frequency of observations.
Connect adjacent dots to create a polygon.
Place a dot along a horizontal scale for each observation.
"Pile up" dots that are too close to show separately.

Answers

The operations to create a dot plot includes A,C and D.

What Exactly Is a Dot Plot?

A dot plot, also known as a strip plot or dot chart, is a simple type of data visualisation in which data points are represented as dots on a graph with x and y axes. These charts are used to graphically represent certain data patterns or groups. The most well-known dot plot is perhaps the Federal Reserve's quarterly interest rate predictions.

Now,

As A dot plot is made up of data points that are represented as dots on a graph with an x- and y-axis. Dot plots are often set up with one axis representing the range of values or categories along which the data points are categorised and a second axis representing the number of data points in each category.

Hence,

The operations to create a dot plot includes A,C and D.

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30c^8d^3 - 3bc^6 d^2 + 6c^8 d divided by 12c^2 d (polynomials divided by monomials written in standard form)

Answers

To divide polynomials by a monomial written in standard form, you can divide each term of the polynomial by the monomial separately. Applying this to the given expression, we get:

(30c^8d^3 - 3bc^6d^2 + 6c^8d) / (12c^2d)

= 30c^8d^3/(12c^2d) - 3bc^6d^2/(12c^2d) + 6c^8d/(12c^2d)

= 2.5c^(8-2)d^(3-1) - 0.25bc^(6-2)d^(2-1) + 0.5c^(8-2)d^(1-1)

= 2.5c^6d^2 - 0.25bc^4d + 0.5c^6

= 5c^6d^2 - 0.5bc^4d + c^6/2

Therefore, the simplified expression is 5c^6d^2 - 0.5bc^4d + c^6/2.

what is 120 kilos in pounds

Answers

The required value of 120 kilos which is same as 120 kilograms is equal to ( 264.55 ) pounds ( round up to two decimals ) .

Kilos is short form of kilogram.Kilograms and pounds both are the standard units of mass.

One kilogram = 2.20462 pounds

We need to convert 120 kilograms into pounds :

⇒ 120 kilograms = ( 120 × 2.20462 ) pounds

⇒ 120 kilograms = ( 264.5544 ) pounds

⇒ 120kilograms = ( 264.55 ) pounds ( round up to two decimals )

Therefore, the value of the 120 kilograms is equal to ( 266.55 ) pounds ( round up to two decimals ) using converting factor.

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Mrs.baxter deposits 2000 into an account that earns 5% simple interest how much is mrs baxters investment worth after 8 years What formula should be used

Answers

Answer: The formula to calculate simple interest is:

I = P * r * t

where:

- I is the interest earned

- P is the principal amount (the initial investment)

- r is the annual interest rate (as a decimal)

- t is the time in years

- To calculate the total amount in the account after the interest is earned, you need to add the interest earned to the principal amount.

So for Mrs. Baxter's investment, the calculation would be:

P = 2000 (the principal)

r = 0.05 (the annual interest rate as a decimal)

t = 8 (the time in years)

I = P * r * t = 2000 * 0.05 * 8 = 800

The interest earned over the 8-year period is $800.

The total amount in the account after 8 years would be the principal plus the interest earned:

A = P + I = 2000 + 800 = 2800

So Mrs. Baxter's investment would be worth $2,800 after 8 years.

Step-by-step explanation:

The amount after 8 years with the rate of interest as 5% simple interest is $2800.

What is meant by simple interest?

Simple interest is a way to figure out how much interest will be charged on a sum of money at a specific rate and for a specific duration of time. Unlike compound interest, where we add the interest of one year's principal to the next year's principal to compute interest, the principal amount under simple interest remains constant. Simple interest is a quick and simple approach to figuring out how much money has accrued interest. Interest is always applied to the original principal amount and is calculated at the same rate for each period of time.

Given,

The principal amount P = $2000

The rate of interest r = 5% = 5/100 = 0.05

The time period t = 8 years.

We have to find the amount after 8 years using simple interest formula.

Amount A = P(1+rt) = 2000(1+0.05 * 8)

= 2000 * 1.4 = $2800.

Therefore the amount after 8 years with the rate of interest as 5% simple interest is $2800.

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1. w/ń (Find the value of): (27)-2/3

Answers

Answer:

26 [tex]\frac{1}{3}[/tex]

Step-by-step explanation:

26 3/3 - 2/3 = 26 1/3

how to convert 152 cm to inches?

Answers

On converting the length , 152 centimeter is equivalent to 59.8424 inches .

There are various units of measuring the length , which include , meter (m) , centimeter (cm) , kilometer (km) , inches (in.) ;

In order to convert 152 centimeters (cm) to inches,

We use the conversion factor of 0.3937 inches per centimeter.

So , we multiply the number of centimeters by this conversion factor to get the equivalent length in inches ;

By using this method, we get ;

⇒ 152 cm × 0.3937 inches/cm = 59.8424 inches ;

Therefore, 152 centimeters is equal to approximately 59.8424 inches.

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An estimate of 24.5% of the water used each day is for cooking. If a family uses 68.6 gallons of water a day for cooking , how many gallons do they use every day?

Answers

They use 280 gallons a day.

24.5 times 2.8 is 68.6

24.5% of 100 is 24.5

100 times 2.8 is 280

I need help finding the answer help me

Answers

Answer:

[tex]y = -\frac{5}{3}x-7[/tex]

Step-by-step explanation:

We are given three coordinates. First, we have to find the slope. We can do this by counting the slope of two points which we will do for simplicity's sake.

[tex]\frac{rise}{run}[/tex] gives us [tex]-\frac{5}{3}[/tex] which we will use as the slope.

Looking at the graph, the y intercept of the equation is -7, so our equation would be [tex]y=-\frac{5}{3}x-7[/tex]

what is 120kg in lb?

Answers

Answer and Step-by-step explanation:

120 kg is approximately 264.55 lbs (pounds).

Let the graph of g be a vertical stretch by a factor of 4 and a reflection in the x-axis of the graph of f(x) =x^2-3. Write a rule for g

Answers

The rule for the graph of g is g(x) = -4(x^2-3). This graph is a vertical stretch by a factor of 4 and a reflection in the x-axis of the graph of f(x) = x^2-3.

Drag the tiles to the correct boxes to complete the pairs.

Find the volume of the cubes or rectangular prisms in cubic centimeters

Answers

The volumes of the given cube and rectangular prisms in cubic centimeters are:

1) Cube with a side length of 2/5 cm: 8/125 cm^3

2) Rectangular prism with a length, width, and height of 3/5 cm, 4/5 cm, and 3/5 cm respectively: 36/125 cm^3

3) Rectangular prism with a length, width, and height of 1/5 cm, 2/5 cm, and 3.5 cm respectively: 6/125 cm^3

4) Cube with a side length of 1/5 cm: 1/125 cm^3

To find the volume of a cube or rectangular prism, you need to use the formula: