Question

Alice runs a website that has gotten quite popular. However, its popularity seems to have peaked, and the site is now getting 8% fewer hits each week. If Alice's site got 42,451 hits this week, how many weekly hits can she expect it to get 10 weeks from now?If necessary, round your answer to the nearest whole number.

Answer 1

The website's hits are dropping at 8% per week. To determine how many weeks she will have in 10 weeks you have to determine an exponential equation:

$y=a(1-r)^x$

Where

x is the time in weeks

r is the decrease rate expressed as a decimal value

a is the initial value

y is the number of hits after x weeks

Considering the starting value a=42,451, and the decrease rate as r=8/100=0.08 you can determine the exponential equation that models this situation as follows:

$\begin{gathered} y=42,451(1-0.08)^x \\ y=42,451(0.92)^x \end{gathered}$

Replace the equation with x=10

$\begin{gathered} y=42,451(0.92)^{10} \\ y=18,440.22\to18,440 \end{gathered}$

She can expect to get 18,440 hits in 10 weeks