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%?

(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

--- Initial Population

--- rate

(A) WHEN THE RATE DECREASES

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

This is given as:

Substitute values for a and r

Convert % to decimal

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

For 1 to 5:

Calculate f(5) and f(1)

For 6 to 10:

Calculate f(6) and f(10)

So, we have:

for year 1 to 5

This means that the number of pikas reduces by 9.36 yearly

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:

Substitute values for a and r

Convert % to decimal

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

For 1 to 5:

Calculate f(5) and f(1)

For 6 to 10:

Calculate f(6) and f(10)

So, we have:

for year 1 to 5

This means that the number of pikas increases by 14.04 yearly

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.

the 2 figures are congruent bc if you reflect abcd over the y axis then over the d axis the figures overlap

answer: c, the green line

step-by-step explanation:

there is no black line, eliminate b.

simple interest implies periodic payments, but the red line shows no payments, eliminate d.

simple interest has equal payments. if paid say every day, the graph is about a straight line (actually a stairstep).

the yellow line is not straight, eliminate a.

check: the green line is straight, answer is c.

simple interest with positive interest rate gives a straight line sloping up to the right. green line:

g(t) = $100 + ($200-$100) ÷ (20 years) × (t years)

= $100 + (4%/year) × ($100)(t years)

incidentally, the yellow line curving upward represents continuously compounded interest

y = $100 × 2^(t years / (14 assuming the yellow line hits $200 at 14 years. 2^0 is 1, so y(0) = $100; 2^(14/14) is 2, so y(14) = $200.