Chapter 6.2, Problem 27E

To determine

To write:A function that represents the situation where a population of 100,000 decreases by 2% each year.

Answer to Problem 27E

  $f(n)=100000{(1-0.02)}^n$

Explanation of Solution

Given:

A population of 100,000 decreases by 2% each year.

A function of the form $f(n)=a{(1-r)}^n$ , where $a>0$ and $0<r<1$ , is an exponential decay function where “a” is the initial amount, “r” is the rate of decay in decimal form and “n” is the time.

Let the function be given by f(n) where n is the n-th year from the initial date.

In the given problem we have $a=100000$ and $r=2\%=\frac{2}{100}=0.02$

Therefore,according to the given problem the function must be defined as $f(n)=100000{(1-0.02)}^n$