Question

traveling carnivals move from town to town, staying for a limited number of days before moving to the next stop. the management of a certain 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 revenue can the carnival anticipate on its 5th night in town? on the 5th night, the carnival can expect $ in revenue.

Explanation:

Step1: Identify the formula for a geometric - sequence

The formula for a geometric sequence is $a_n=a_1r^{n - 1}$, where $a_1$ is the first - term, $r$ is the common ratio, and $n$ is the term number. Here, $a_1 = 15000$, $r=0.75$, and $n = 5$.

Step2: Substitute the values into the formula

$a_5=15000\times(0.75)^{5 - 1}$.

Step3: Calculate $(0.75)^4$

$(0.75)^4=0.75\times0.75\times0.75\times0.75 = 0.31640625$.

Step4: Calculate $a_5$

$a_5=15000\times0.31640625=4746.09375\approx4746$.

Answer:

4746