How would the average rate of change over years 1 to 5 and years 6 to 10 be affected if the population increased at a rate of 8%?

Answers

Answer 1

Answer:

(A): As year increases the number of pikas reduces.

(B): As year increases the number of pikas increases as opposed to when the rate reduces.

Step-by-step explanation:

See comment for complete question

Given

[tex]a = 144[/tex] --- Initial Population

[tex]r = 8\%[/tex] --- rate

(A) WHEN THE RATE DECREASES

First, we need to write out the function when the population decreases.

This is given as:

[tex]f(x) = a(1-r)^x[/tex]

Substitute values for a and r

[tex]f(x) = 144(1-8\%)^x[/tex]

Convert % to decimal

[tex]f(x) = 144(1-0.08)^x[/tex]

[tex]f(x) = 144(0.92)^x[/tex]

Next, we calculate the average rate of change for both intervals using:

[tex]Rate = \frac{f(b) - f(a)}{b-a}[/tex]

For 1 to 5:

[tex]Rate = \frac{f(5) - f(1)}{5-1}[/tex]

[tex]Rate = \frac{f(5) - f(1)}{4}[/tex]

Calculate f(5) and f(1)

[tex]f(x) = 144(0.92)^x[/tex]

[tex]f(1) = 144*0.92^1 =144*0.92=132.48[/tex]

[tex]f(5) = 144*0.92^5 =144*0.66=95.04[/tex]

[tex]Rate = \frac{95.04 - 132.48 }{4}[/tex]

[tex]Rate = \frac{-37.44}{4}[/tex]

[tex]Rate = -9.36[/tex]

For 6 to 10:

[tex]Rate = \frac{f(10) - f(6)}{10-6}[/tex]

[tex]Rate = \frac{f(10) - f(6)}{4}[/tex]

Calculate f(6) and f(10)

[tex]f(x) = 144(0.92)^x[/tex]

[tex]f(6) = 144*0.92^6 =144*0.61=87.84[/tex]

[tex]f(10) = 144*0.92^{10} =144*0.43=61.92[/tex]

[tex]Rate = \frac{61.92-87.84}{4}[/tex]

[tex]Rate = \frac{-25.92}{4}[/tex]

[tex]Rate = -6.48[/tex]

So, we have:

[tex]Rate = -9.36[/tex] for year 1 to 5

This means that the number of pikas reduces by 9.36 yearly

[tex]Rate = -6.48[/tex] for year 6 to 10

This means that the number of pikas reduces by 6.48 yearly

So, we can say that, as year increases the number of pikas reduces.

(B) WHEN THE RATE INCREASES

First, we need to write out the function when the population decreases.

This is given as:

[tex]f(x) = a(1-r)^x[/tex]

Substitute values for a and r

[tex]f(x) = 144(1+8\%)^x[/tex]

Convert % to decimal

[tex]f(x) = 144(1+0.08)^x[/tex]

[tex]f(x) = 144(1.08)^x[/tex]

Next, we calculate the average rate of change for both intervals using:

[tex]Rate = \frac{f(b) - f(a)}{b-a}[/tex]

For 1 to 5:

[tex]Rate = \frac{f(5) - f(1)}{5-1}[/tex]

[tex]Rate = \frac{f(5) - f(1)}{4}[/tex]

Calculate f(5) and f(1)

[tex]f(x) = 144(1.08)^x[/tex]

[tex]f(1) = 144(1.08)^1 = 144*1.08= 155.52[/tex]

[tex]f(5) = 144(1.08)^5 = 144*1.47= 211.68[/tex]

[tex]Rate = \frac{211.68 - 155.52}{4}[/tex]

[tex]Rate = \frac{56.16}{4}[/tex]

[tex]Rate = 14.04[/tex]

For 6 to 10:

[tex]Rate = \frac{f(10) - f(6)}{10-6}[/tex]

[tex]Rate = \frac{f(10) - f(6)}{4}[/tex]

Calculate f(6) and f(10)

[tex]f(x) = 144(1.08)^x[/tex]

[tex]f(6) = 144(1.08)^6 = 228.52[/tex]

[tex]f(10) = 144(1.08)^{10} = 310.89[/tex]

[tex]Rate = \frac{310.89-228.52}{4}[/tex]

[tex]Rate = \frac{82.37}{4}[/tex]

[tex]Rate = 20.59[/tex]

So, we have:

[tex]Rate = 14.04[/tex] for year 1 to 5

This means that the number of pikas increases by 14.04 yearly

[tex]Rate = 20.59[/tex] for year 6 to 10

This means that the number of pikas increases by 20.59 yearly

So, we can say that, as year increases the number of pikas increases as opposed to when the rate reduces.


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Math

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Step-by-step explanation:

Step 1: Define

sin∠C

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Step-by-step explanation:

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Answers

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Answers

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Answers

Here are the steps I took to solve it. Hopefully you understand what I wrote

50 PTSSSSSSSSSSSSSSSSSS
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Step-by-step explanation:

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Step-by-step explanation:

Given

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Step-by-step explanation:

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-4, 12, -36, 108,...

a
a_n=-4·(-3)^{n-1}

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Step-by-step explanation:

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Step-by-step explanation:

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Step-by-step explanation:

Given

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Step-by-step explanation:

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Answer:

The answers are:

Step-by-step explanation:

1)Adjacent

2)Vertical

3)Corresponding

4)None of these

5)1,7  3,5  4,6  2,8 (<--angle numbers)

6)4,5  2,7 (<--angle numbers)

7)1=85, 2=95, 3=85, 4=85

8)1=60, 2=120, 3=60, 4=120

9)1=90, 2=90, 3=90, 4=90

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Answer:

1.

adjacent

2.

vertical

3.

corresponding

4.

none (just regular interior and thats not an option)

5.

(<5,<7) (<6,<8) (<1,<3) (<2,<4)

6.

(<2,<7) (<6,<3)

7.

<1= 85

<2= 95

<3= 85

<4= 85

8.

<1= 60

<2= 120

<3= 60

<4= 120

9.

<1= 90

<2= 90

<3= 90

<4= 90

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What are the resulting equations?

Answers

Answer:

14x + 6y = 10

14x + 35y = -77

Step-by-step explanation:

Multiply the top one by 2

14x + 6y = 10

Multiply the bottom one by 7

14x + 35y = -77

His next step is to subtract. You could have done this by multiplying the top one by -2

-14x - 6y = - 10

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Answer:

A) 14x + 6y = 10

-14x - 35y = 77

Step-by-step explanation:

multiple the first equation by 2 and the second equation by -7

2( 7x + 3y = 5)

-7( 2x + 5y = -11)


14x + 6y = 10

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Answers

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Step-by-step explanation:

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Answers

Answer:

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