Question

traveling carnivals usually shut down for the winter months. suppose a traveling carnival decided to instead remain open for business indefinitely in its last stop of the season. assume its usual revenue projections hold ($15,000 on the first night, and each nights revenue after the first night will be about 75% of the previous nights revenue). to the nearest dollar, what is the maximum amount of revenue the carnival can expect in this town? $58,931 $60,000 $1,125,000 since they are staying open indefinitely, there is no limit to their revenue.

Explanation:

Step1: Identify the series type

This is an infinite geometric - series problem. The first - term $a = 15000$ and the common ratio $r=0.75$.

Step2: Apply the formula for the sum of an infinite geometric series

The formula for the sum of an infinite geometric series is $S=\frac{a}{1 - r}$, where $|r|\lt1$.
Substitute $a = 15000$ and $r = 0.75$ into the formula: $S=\frac{15000}{1 - 0.75}$.

Step3: Calculate the sum

$S=\frac{15000}{0.25}=60000$.

Answer:

$60000$