The population of a pigeons in a city is 100 and is growing exponentially at 20% per year. Write a function to represent the population of pigeons after
t
t years, where the monthly rate of change can be found from a constant in the function. Round all coefficients in the function to four decimal places. Also, determine the percentage rate of change per month, to the nearest hundredth of a percent

Answers

Answer 1

Answer:

p(t) = 100×1.0153^(12t)1.53% per month

Step-by-step explanation:

In general, the function will be written ...

  p(t) = (initial value)×(growth factor)^t

where t is in units comparable to those applicable to the growth factor. The growth factor is found from ...

  growth factor = 1 + growth rate

Here, the growth rate is given as 20% per year, so the growth factor per year is ...

  1 +20% = 1.20

The initial value is given as 100, so we can write the exponential function as ...

  p(t) = 100×1.20^t

__

The time period units for t are supposed to be years, but we want to find the growth rate for a month. We can do that by recognizing there are 12 months in a year. In the above equation, we can use (1/12)(12t) in place of t, then figure the growth factor (and growth rate) per month.

  p(t) = 100×(1.20^(1/12))^( 12t)

  p(t) = 100×1.0153^(12t) . . . . population exponential function

This shows the monthly growth factor is 1.0153, so the monthly rate of change (growth rate) is ...

  1.0153 -1 = 0.0153 = 1.53% . . . . monthly rate of change

Answer 2

Answers:

Function is [tex]P(t) = 100(1.0153)^{12t}\\\\[/tex]Monthly growth rate is roughly 1.53%

=====================================================

Explanation:

The population starts at 100 pigeons. After a year, the population goes up by 20%, meaning the population goes up by 20. It lands on 120 after a full year (100+20 = 120).

Dividing the "before" and "after" population amounts gets us 120/100 = 1.20

If we didn't worry about the monthly rate, and only cared about the annual rate of growth, then the population function would be

[tex]P(t) = 100(1.20)^t[/tex]

where t is the number of years and P(t) is the population for that year number. Notice how the 1.20 is the base of the exponential to quickly tell the reader the annual rate of growth. We read off the .20 portion and that converts to 20% after moving the decimal 2 spots to the right.

If we were to plug t = 0 into that function, then we'd get P(0) = 100. Inputting t = 1 leads to P(1) = 120. This helps confirm we have the correct annual growth rate function.

---------------------

Unfortunately, your teacher doesn't want the annual growth rate function. Instead, they want you to write a function where the reader can easily pick out the monthly rate of change without having to do any math. This is due to the instructions that "the monthly rate of change can be found from a constant in the function". Let m be this constant.

Since t is the number of years, this means t = 1/12 represents 1/12 of a year, aka 1 month. If you were to compute P(1/12), then you should get roughly 101.530947049973

Divide this amount over the initial population to find m.

m = 101.530947049973/100 = 1.01530947049973

So we get m = 1.0153 after rounding to four decimal places.

The number m is in the form 1+x. Solving 1+x = m will lead to x = 0.0153 to indicate a monthly rate of change is roughly 1.53% since we move the decimal point 2 spots to the right to go from 0.0153 to 1.53%

The pigeon population is increasing by roughly 1.53% each month.

This is why computing this m value leads to the reader able to spot the monthly rate of change without having to resort to a calculator. All they have to do is read the digits to the right of the decimal point and convert that to percentage form.

---------------------

An alternative way to compute this value is to use this formula

m = (1+r)^(1/12)

We'll plug in the annual rate r = 0.20 to get:

m = (1+r)^(1/12)

m = (1+0.20)^(1/12)

m = 1.01530947049973

m = 1.0153

We get the same approximate value as earlier.

---------------------

Whichever method you use, you should get roughly m = 1.0153

We're given that A = 100 is the initial population

So we'll then be able to form this function

[tex]P(t) = A*(m)^{12t}\\\\P(t) = 100(1.0153)^{12t}\\\\[/tex]

This represents the monthly growth of the population where t is in years. Note that after something like t = 3 years, we have 12t = 12*3 = 36 months pass by. So that's why the 12t is in the exponent rather than simply t.

Once again, for comparison we have...

[tex]P(t) = 100(1.20)^{t}\\\\[/tex] for annual growth[tex]P(t) = 100(1.0153)^{12t}\\\\[/tex] for monthly growth

Each function has t represent the number of years. The difference is the base of each exponential to tell us the respective annual or monthly growth rate. Also, the exponent up top must be adjusted depending on which you go for.

---------------------

You may be wondering: "what if the exponent in the monthly growth rate function wasn't 12t?". Let's find out. We'll assume the monthly growth rate function is [tex]P(t) = 100(1.0153)^{t}\\\\[/tex] and show that an error happens.

If we plugged in something like t = 1, we should get P(t) = 120 like mentioned earlier.

[tex]P(t) = 100(1.0153)^{t}\\\\P(1) = 100(1.0153)^{1}\\\\P(1) = 100(1.0153)\\\\P(1) = 101.53\\\\[/tex]

That value of 101.53 is the approximate population number after 1 month, rather than 1 year. Making the exponent 12t will fix the issue.


Related Questions

I need help anyone please help.

Answers

Answer:

1/4 or 1/2 good luck my  guy

Step-by-step explanation:

Which substances will make a salt when combined?
Question 6 options:

Vinegar and soda

Soda and wine

Detergent and ammonia

Fertilizer and vinegar

Answers

A.Vinegar and soda

-A salt is a substance that contains a cation which is a metal ion or an ammonium ion and an anion derived from an acid. It is an ionic compound that can be formed by the neutralization reaction of an acid and a base.

-For example; a reaction between a soluble base sodium hydroxide and an acid dilute sulfuric acid results to the formation of salt sodium salt. There are also other methods of generating a cell apart from neutralization, such as precipitation reactions and direct synthesis among others,

On a coordinate plane, a line is drawn from point A to point B. Point A is at (negative 4, 8) and point B is at (2, negative 4). What are the x- and y-coordinates of point C, which partitions the directed line segment from A to B into the ratio 3:10? Round to the nearest tenth, if necessary. X = y =.

Answers

The x and y coordinates of point C are -2.6 and 5.2, respectively

The coordinate of the points are given as:

[tex]A = (-4,8)[/tex]

[tex]B =(2,-4)[/tex]

The ratio is given as:

[tex]m :n = 3 : 10[/tex]

The point at the given ratio is calculated as:

[tex]C = (\frac{mx_2+nx_1}{m+n},\frac{my_2+ny_1}{m+n})[/tex]

So, we have:

[tex]C = (\frac{3 \times 2 + 10 \times -4}{3+10},\frac{3 \times -4 +10 \times 8}{3+10})[/tex]

Simplify

[tex]C = (\frac{-34}{13},\frac{68}{13})[/tex]

[tex]C = (-2.6,5.2)[/tex]

Hence, the x and y coordinates of point C are -2.6 and 5.2, respectively

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Answer:

a

Step-by-step explanation:

if a car travels for 3 hours its average speed is 75km/h work out the total distance the car travels

Answers

Answer:

225 km

Step-by-step explanation:

75 · 3 = 225

Answer:

225 km

Step-by-step explanation:

Distance = Speed × Time

Distance = 75km/h × 3

Distance = 225km

What is the equation of the line in standard form?​

Answers

(2,2)

Step-by-step explanation:

You have to add them together and minus the negatives

A car is 200 inches long the truck is 50% longer than the car how long is the truck

Answers

Answer:

300

Step-by-step explanation:

This question is pretty simple.

First, we just have to find 50% of 200.

So 50% is also 1/2.

1/2 of 200 is just 100. The question says that the truck is 50% LONGER than the car.

So 50% longer is 100 and 100+200(the length of the car) is 300.

The answer.

what is 5 7/20 written as a decamal

Answers

Answer:

5 7/20 as a decimal is 5.35

Hope that helps. x

Answer:

Step-by-step explanation:

If your question has a big number 5 and a fraction 7/20, the 5 is going to be in the left side of the decimal, like 5.something ... the 7/20 is going to be the part on the right. If you're allowed to use a calculator just divide 7÷20 and that part goes on the right of the decimal. If you're not allowed to use a calculator then change 7/20 into something/100 ... 7/20× 5/5 gives you 35/100. That is the decimal part. It is written .35 So all together you get 5 7/20 is 5.35

Question 14 (5 points)
image

Which of the following is a true statement about the rhombus shown?
Question 14 options:

A)



B)

m∠SPQ = 90°

C)

m∠STP = 90°

D)





Question 15 (5 points)
image

Determine the value of x.
Question 15 options:

A)

x = 90°

B)

x = 45°

C)

x = 20°

D)

x = 4.5°

Answers

Answer:

14) C

15) D, because 90:20=4.5

I need help final exam will mark brainliest...
Pablo is walking. The number of minutes he has walked varies directly with the number of calories he has burned. See the graph below. two-part question.


(a) How many calories is Pablo burning per minute?

(b) what is the slope of the graph?

Answers

5 calories per minute
1/2 is your slope.

Answer:

1. 5 calories per minute

2.1/2 is your slope.

Step-by-step explanation:

plz help ppl keep putting links

Answers

Answer:

∠DAB=140

∠BAC=60

∠EBF=40

∠ACB=80

∠BCG=100

Step-by-step explanation:

0.41g -2) + 1.2 =-(g-1) + 2.9​

Answers

Answer:

g=-3repeated

Step-by-step explanation:

Rewrite this problem combining like terms!!
2 m − 3 m + 4

Answers

i believe the answer is 4-m! hopefully it’s right, sorry if it’s not!

hidffhhhhhhhhhhhhhhhhhhhhhhhhhd

Answers

Yes that is the right thing

5. (27:21) Harry says there are 5 families gone on
one block alone. If there are 12 families on that
block, how many families might you expect to be
gone on a street with 60 families?

Answers

Based on the number of families that left and the number in total on that block, the expected number of families gone on the other block is 25 families.

On the first block, the proportion of families that is gone is:

= Number of families gone / Total number of families on block

= 5 / 12

If there are 60 families on a block, the number gone would be:

= Proportion of families gone x Total number of families

= 5/12 x 60

= 25 families

In conclusion, 25 families would be gone

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a train which is 100 meters long is traveling at a speed of 90km per hour. How many seconds will it take for this train to pass completely through a 300 meter tunnel

Answers

The train will take 16 seconds to pass completely through a 300 meter tunnel.

Let suppose that the train moves itself at constant velocity, the vehicles needs to cover the tunnel length ([tex]L[/tex]) and its length ([tex]l[/tex]), both in meters, to pass through the tunnel, the time taken by the train ([tex]t[/tex]) is described by the following kinematic formula:

[tex]t = \frac{L+l}{v}[/tex] (1)

Where [tex]v[/tex] is the train velocity, in meters per second.

If we know that [tex]L = 300\,m[/tex], [tex]l = 100\,m[/tex] and [tex]v = 90\,\frac{km}{h}\,\left(25\,\frac{m}{s} \right)[/tex], then the time taken by the train is:

[tex]t = \frac{300\,m + 100\,m}{25\,\frac{m}{s} }[/tex]

[tex]t = 16\,s[/tex]

The train will take 16 seconds to pass completely through a 300 meter tunnel.

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What is the slope of a line perpendicular to the line whose equation is x-y=6x−y=6. Fully simplify your answer.

Answers

It should by the answer but if not sorry
Answer:
(X,Y)
(0,6)

what number set does -7 belong to

Answers

Answer:

Integers

Step-by-step explanation:

Integers include both positive and negative numbers. This is the simplest answer. This set doesn't include any fractions or decimals. Integers are a subset of rational numbers, which are a subset of real numbers, which are a subset of complex numbers.

Can you please help me find number for D

Answers

Step-by-step explanation:

the slope of the line between the first 2 points must be the same as the slope between the second and the third point.

the slope is y difference / x difference.

so,

b/a = d/c

-3/1.6 = d/1.5

d = -3×1.5 / 1.6 = -4.5 / 1.6 = -2.8125

PLEASEEE HURRY. Please I really need this please

Answers

Answer:

answer is

Step-by-step explanation:

Answer:

final answer is: ABC, A (-5,1), B (-4,6) and C (-1,4)

Step-by-step explanation:

Original: ABC, A (2,-1), B (1,4) and C (-2,2)

translate 3 units to the right and 2 units up: ABC, A (5,1), B (4,6) and C (1,4)

reflected over the x-axis: ABC, A (5,-1), B (4,-6) and C (1,-4)

rotated 180°: ABC, A (-5,1), B (-4,6) and C (-1,4)

Help a girl out pls!!!

Answers

Answer: AA Similarity

Step-by-step explanation:

Since both shapes have two corresponding angles that are congruent, AA similarity is applied here.

The temperature at 7:00 a.m, was 12 C, and by 7:00 p.m, it had dropped
to -10°C. Which expression represents the change in temperature:

(A 12 + (-10)

(B 12 - 10

(C -10 + 12

(D -10 - 12

Answers

Answer:  D    -10 - 12

Step-by-step explanation:

Temperature change is (Final T) - (Initial T)

(Final T) = -10C

(Initial T) =  12

(Final T) - (Initial T) = -10C - 12C

Temp Change - 22C

- 12 \geq - 2 x - 15
[tex] - 12 \geqslant - 2x - 15[/tex]
what is this answer??? plssss help gotta get it done by tomorrow ​

Answers

Answer:

x= -3/5

Step-by-step explanation:

-12>= -2x-15

add 15 to both sides 3>= -2xdivide by -23/-2=x

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Answers

Step-by-step explanation:

VW to WY have the ratio 3/2.

VX to XZ must have the same ratio.

and VX > VW.

so,

30 and 20 is possible, as 30/20 = 3/2.

3 and 2 is not possible, because 6 > 3.

27 and 18 is possible, as 27/18 = 3/2.

13.2 and 8.8 is possible, 13.2/8.8 = 3/2.

8.7 and 5.7 is not possible, as 8.7/5.7 is not 3/2.

8.7/3 = 2.9

but 2.9×2 = 5.8 and not 5.7.

Write an inequality to compare the ratios 2/4 and 5/6.

Answers

Answer:

5/6>2/4

Step-by-step explanation:

5/6 is greater than 2/4

what will be the total surface area of a cylinder if

h = 22cm
and
r = 3cm
TSA = ?

Please give me the answer plssss??

Answers

Answer:

total surface area of a cylinder is 471 cm²

Help me please

H please

Answers

Answer:

pi

Step-by-step explanation:

Can you explain how you got the answe

Answers

Answer:

3

Step-by-step explanation:

she put 4 stickers on each car

someone please explain this

Answers

Answer:

HOPE THIS HELPS

Step-by-step explanation:

[tex]x^{2}[/tex]-14x-32 =(X+2)(X-16)

A=1

B=2

C=1

D=-16

Have students write the answer to the Essential Question and draw examples to explain their answer

Answers

What’s the question?

Krista's snow fort has an area of 6228 sq inches if it is 72 in long what is the width

Answers

Answer:

86.5 inches

Step-by-step explanation:

6228 / 72 = 86.5

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