Question

3) In 2010, there were approximately 21 million Amazon Prime members. The number of memberswas approximately 68 million by 2015. Write an exponential model that represents the number ofAmazon Prime members, where t represents the number of 5-year time periods since2010. The base (b) of your exponential model should be correct to three places after the decimalpoint.

Answer 1

From the question, we can deduce that there was an exponential growth between 2010 and 2015 at Amazon Prime. So let's go ahead and write write the required exponential model, it is given thus;

$y=ab^x^{}$

Where y = ending value (the amount after growth have happened = 68 million

a = initial value = 21 million

b = growth factor

x = the number of time intervals that have passed = 5

So, if we go ahead and substitute the above given values in our equation, we'll have;

$68000000=21000000(b)^5$

Let's divide both sides of the equation with 21000000 and go ahead to find b;

$\begin{gathered} \frac{68000000}{21000000}=\frac{21000000b^5}{21000000} \\ b^5=3.238 \end{gathered}$

To find b, we have to find the fifth root of both sides;

$\begin{gathered} b=\sqrt[5]{3.238} \\ \therefore b=1.265 \end{gathered}$

Therefore, the growth factor, b, is 1.265 (to 2 decimal places)