Question

Solve the problem of exponential growth. In 1985 an antique automobile club had 23,000 members. Since then its membership has grown at an average rate of 5% per year. Assuming this trend continues, how many members will there be in 2020? Round to the nearest thousand.

Answer 1

`127,000\ members`

Explanation:

In this problem we have an exponential function of the form

`f(x)=a(b)^(x)`

where

a is the initial value

b is the base

The base is equal to

b=1+r

r is the average rate

In this problem we have

a=23,000 members

r=5%=5/100=0.05

b=1+0.05=1.05

substitute

`f(x)=23,000(1.05)^(x)`

x ----> is the number of years since 1985

How many members will there be in 2020?

x=2020-1985=35 years

substitute in the function

`f(x)=23,000(1.05)^(35)=126,868\ members`

Round to the nearest thousand

`126,868=127,000\ members`