Chapter 11.3, Problem 85STP

To determine

Find the number of customer the store should expect.

Answer to Problem 85STP

The store should expect around 731 customers.

Explanation of Solution

Given:

A certain store found that the number of customers who will attend a sale can be modeled by $N=125·\sqrt[3]{100Pt}$ , where N is the number of customers expected, P is the percent of sale discount, and t is the number of hours the sale will last. Find the number of customers the store should expect for a sale that is 50% off and will last four hours.

Concept Used:

To find the total number of expected customer, substitute $P=0.5\text{and}t=4$ in the function given in the question $N=125·\sqrt[3]{100Pt}$

Calculation:

  $\begin{array}{l}N=125·\sqrt[3]{100Pt}\\ N=125·\sqrt[3]{100·0.5·4}[\text{substitute}P=0.5\text{and}t=4]\\ N=125·\sqrt[3]{200}\\ N\approx 730.9\end{array}$

Thus, the store should expect around 731 customers.