Question

1. communication cell phone usage grew about 23% each year from 2010 to 2016. if cell phone usage in 2010 was 43,000,000, write a function to model u.s. cell phone usage over that time period. then estimate the cell phone usage in 2013. round to the nearest ten thousand.

Explanation:

Step1: Define exponential growth model

The general exponential growth function is $U(t) = U_0(1 + r)^t$, where $U_0$ is the initial value, $r$ is the annual growth rate, and $t$ is the number of years after 2010.

Step2: Plug in known values

Here, $U_0 = 43000000$, $r = 0.23$. So the model is $U(t) = 43000000(1 + 0.23)^t = 43000000(1.23)^t$.

Step3: Calculate $t$ for 2013

2013 is 3 years after 2010, so $t = 3$.

Step4: Compute usage in 2013

Substitute $t=3$ into the model:
$$U(3) = 43000000(1.23)^3$$
First calculate $(1.23)^3 = 1.23\times1.23\times1.23 = 1.860867$
Then $U(3) = 43000000\times1.860867 = 79917281$

Step5: Round to nearest ten thousand

Round 79917281 to the nearest ten thousand: 79920000

Answer:

The function modeling cell phone usage is $U(t) = 43000000(1.23)^t$ where $t$ is the number of years after 2010.
The estimated cell phone usage in 2013 is 79920000.