Chapter 13.2, Problem 93E

Sales The rate of sales of your company’s Jackson Pollock Advanced Paint-by-Number sets can be modeled by

$s\left(t\right)=\frac{900e^{0.25t}}{3+e^{0.25t}}$ sets per month

t months after their introduction. Find an expression for the total number of paint-by-number sets $S\left(t\right)$ sold t months after their introduction, and use it to estimate the total sold in the first 12 months. [HinT: See Example 5.]