Exponential Growth Rate

Question

In​ 2012, the population of a city was

5.27

million. The exponential growth rate was

1.47​%

per year.

​a) Find the exponential growth function.

​b) Estimate the population of the city in 2018.

​c) When will the population of the city be

7

​million?

​d) Find the doubling time.

Answer 1

The general format of exponential growth is P(t)=P(0)*(1+r)^t. In this case, for part a, replace the general terms with the specific numbers that you know. We know the growth rate is 1.47% and the initial population is 5.27 million.

As a note here, when you are using percents in an equation, you need to convert it to decimal notation first. This means just dividing the percent by 100%.

As another note, we are treating the year 2012 as "Year 0", and since 2013 is "one year after the year we're starting with", 2013 is treated as "year 1". This concept will be necessary for parts b and c.