Chapter 8.7, Problem 8DE

Global Mobile Data Traffic. The amount of data transferred using mobile devices is expected to increase exponentially from 7.2 exabytes per month in 2016 to 49 exabytes per month in 2021.

a. Let $P\left(t\right)=P_0{e}^{kt}$, where $P\left(t\right)$ is the global mobile data traffic, in exabytes per month, t years after 2016. Then $t=0$ corresponds to 2016 and $t=5$ corresponds to 2021. Use the data points (0, 7.2) and (5, 49) to find the exponential growth rate and then the exponential growth function.

b. Use the function found in part (a) to estimate the global mobile data traffic per month in 2019.

c. Assuming exponential growth continues at the same rate, predict the year in which the global mobile data traffic will be 100 exabytes per month.