Exercise 14 Page 525

Practice makes perfect

Let's start with reviewing the exponential growth function.

y=a(1+r)^tHere, a is the initial value, r is the rate of growth, and t is the time. We are told that there were 135 000 deer in 1995, which is the initial value a. Since 1995, the number of whitetail deer has increased at an annual rate of about 10 %, so r= 0.1. Let's substitute these values into the formula. y= 135 000(1+ 0.1)^t We will add the terms inside the parentheses so that the equation is written in the simplest form. y=135 000(1.1)^t This function models the number of whitetail deer in that region t years after 1995.

To calculate the number of whitetail deer that inhabited the region in 2000, let's use the function from Part A.

y=135 000(1.1)^t As we recall, t represents the number of years after 1995. Let's substitute t with 5, which is the number of years from 1995 to 2000, and solve equation for y.

y=135 000(1.1)^t

Substitute

t= 5

y=135 000(1.1)^5

CalcPow

Calculate power

y=135 000(1.61051)

Multiply

y=217 418.85

RoundInt

Round to nearest integer

y≈ 217 419