Chapter 6.1, Problem 46E

Flow rates in the Spokane River The daily discharge of the Spokane River as it flows through Spokane, Washington, in April and June is modeled by the functions

$\begin{array}{lll}{r}_1(t)\hfill & =\hfill & 0.25t^2+37.46t+722.47(\text{April})\text{and}\hfill \\ r_2(t)\hfill & =\hfill & 0.90t^2-69.06t+2053.12(\text{June}),\hfill \end{array}$

where the discharge is measured in millions of cubic feet per day and t = 1 corresponds to the first day of the month (see figure).

1. a. Determine the total amount of water that flows through Spokane in April (30 days).
2. b. Determine the total amount of water that flows through Spokane in June (30 days).
3. c. The Spokane River flows out of Lake Coeur d’Alene, which contains approximately 0.67 mi³ of water. Determine the percentage of Lake Coeur d’Alene’s volume that flows through Spokane in April and June.