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

Answer:

$127,000\ members$

Step-by-step 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

$126,868=127,000\ members$