Question

Help me pleasee :(

The fox population in a certain region has an annual growth rate of 7 percent per year. It is estimated that the population in the year 2000 was 23600.

(a) Find a function that models the population t years after 2000 (t=0 for 2000).
Your answer is P(t)=-------------

(b) Use the function from part (a) to estimate the fox population in the year 2008.
Your answer is (the answer should be an integer) -------------

Answer 1

Part (a)

Answer: P(t) = 23600*(1.07)^t

Step-by-step explanation:

Exponential functions take on the form y = a*b^x

• a = starting amount
• b = growth or decay factor

We have a = 23600 as the starting population. We also have b = 1.07 to represent exponential growth of 7%.

Growth happens whenever b > 1.

If 0 < b < 1, then we'd have decay.

Side note: You can think of the 1.07 as 1 + 0.7 = 100% + 7%

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

Part (b)

Answer: 40549

Step-by-step explanation:

The variable t is the number of years since 2000.

The year 2008 is represented by t = 8 (because 2008-2000 = 8).

Plug this into the function we found earlier.

P(t) = 23600*(1.07)^t

P(8) = 23600*(1.07)^8

P(8) = 23600*(1.71818617983192)

P(8) = 40549.1938440333

P(8) = 40549

We round to the nearest integer or whole number, since we cannot have a fractional amount of foxes. This value is an estimate since we're extrapolating into the future.