princesskeelah
Hi I am currently doing a paper but I don't understand how to do the questions. The following question is the most challenging:
The number of cell phone users in a small town is thought to have increased according to the exponential growth model. Initially in 2014, there were 10,000 users.
a. Assuming a growth rate of 20%, how many users should there be by the end of 2017?
b. New data indicates that there were 18,225 users in 2016.
Determine the new growth rate using this added information.
Hi
princesskeelahWelcome to GMATClub!
a. In order to solve this part of the question, we should simply multiply the number
of users(of a previous year) with 1.2 to get the number of users of the current year.
Going by that at the end of 2015, you will have 1.2*10000 or 12000 users
At the end of 2016, you will have 1.2(12000) = 14400 users
At the end of 2017, you will have 1.2(14400) = 17280 users
b. Since the new data shows that there were 18255 users in 2016 as opposed to the
14400 users if the growth rate was 20%, we know that the growth rate is greater
than 20. Let's call it x
\(10000(1 + \frac{x}{100})(1 + \frac{x}{100}) = 18255\)
\((1 + \frac{x}{100})^2 = \frac{18255}{10000}\)
\((100 + x)^2 = 18255\) -> \((100 + x) = \sqrt{18255} = 135\)(approximately)
Therefore, the new growth rate must be 35%(as per the new data)
Hope this helps you!