Question

suppose a traveling carnival knows that, each time it opens in a new town, it can expect to bring in about $15,000 in revenue the first night. each night after the first, revenue will be about 75% of the previous nights revenue. to the nearest dollar, about how much total revenue would the carnival expect after spending two weeks (14 days) in the town? $210,000 $58,575 $58,931 $15,750

Explanation:

Step1: Identify the geometric - series formula

The sum of a geometric series is given by $S_n=\frac{a(1 - r^n)}{1 - r}$, where $a$ is the first - term, $r$ is the common ratio, and $n$ is the number of terms. Here, $a = 15000$, $r=0.75$, and $n = 14$.

Step2: Substitute the values into the formula

$S_{14}=\frac{15000(1 - 0.75^{14})}{1 - 0.75}$.
First, calculate $0.75^{14}$. Using a calculator, $0.75^{14}\approx0.00332$.
Then, $1-0.75^{14}=1 - 0.00332 = 0.99668$.
Next, $15000\times0.99668 = 14950.2$.
Finally, $\frac{14950.2}{0.25}=59800.8$.

Answer:

$\$58931$ (The closest value to the calculated result among the given options)