AP Calculus AB · Unit 7 · Differential Equations

Let $W(t)$ be the number of pounds of ice in a store's ice chest $t$ hours after the store opens, for $0 \le t \le 10$. The amount of ice satisfies the differential equation $$\frac{dW}{dt} = -0.075\,W,$$ and $W(0) = 12$.

(a) Find $\frac{dW}{dt}$ at $t = 0$, using the differential equation above and the initial amount of ice in the chest. Indicate units of measure.
(b) Use separation of variables to find $W(t)$, the particular solution to the differential equation with initial condition $W(0) = 12$.
(c) The rate at which ice melts is $-\dfrac{dW}{dt}$ pounds per hour. Write, but do not evaluate, an integral expression, in terms of $t$, that gives the number of pounds of ice that melt from $t = 2$ to $t = 6$ hours.
(d) Find the amount of ice remaining in the chest at $t = 8$ hours.