In 2000, a company had 1140 stores nationwide. By 2002, this total had grown to 1538. If the number of stores continues to grow exponentially at the same rate, how many stores will there be in 2016?

Question

In 2000, a company had 1140 stores nationwide. By 2002, this total had grown to 1538. If the number of stores continues to grow exponentially at the same rate, how many stores will there be in 2016?

Answer 1

For exponential growth we use the formula for a geometric sequence

A(n) = A x r^t where A is the initial value, r is the geometric ratio or growth rate in their problem t is time and A(n) is the value at any given time

We have to start by solving for r

We know t=2 2000 - 2002 is 2 years

So 1538 = 1140 x r^2

r^2 = 1538/1140

r= 1.1615

Now that we know r we can calculate the value in the 16 years which have elapsed from 2000 to 2016

A = 1140 x 1.1615^16 = 12,511