Question

at the end of the holiday season in january, the sales at a department store are expected to fall. it is estimated that for the x day of january the sales will be $s(x)=2+\frac{9}{(x + 1)^2}$ thousand dollars.
a) find the total sales for january 9 and determine the rate at which sales are falling on that day.
b) compare the rate of change of sales on january 2 to the rate on january 9. what can you infer about the rate of change of sales?
a) the total sales for january 9 were (square) thousand dollars.
(round to three decimal places as needed.)

Explanation:

Step1: Substitute \(x = 9\) into \(S(x)\)

Given \(S(x)=2+\frac{9}{(x + 1)^{2}}\), when \(x = 9\), we have \(S(9)=2+\frac{9}{(9 + 1)^{2}}\).
First, calculate \((9 + 1)^{2}=100\). Then \(\frac{9}{100}=0.09\). So \(S(9)=2 + 0.09=2.09\).

Answer:

\(2.090\)