Water draining from a tank — AP® Calculus AB

Name: ______________________ Date: ____________ Water draining from a tank (9 points)

Table

The depth h of water in the tank, in feet, t minutes after the hole is opened, satisfies the differential equation in the table
Quantity	Value
$\frac{dh}{dt}$	$-\frac{1}{5}\sqrt{h}$ feet per minute
$h(0)$	16 feet

(a) Use the line tangent to the graph of $h$ at $t = 0$ to approximate the depth of the water at $t = 1$ minute. [2 points]
(b) Find $\frac{d^2h}{dt^2}$ in terms of $h$ . Determine whether the approximation in part (a) is an overestimate or an underestimate. Give a reason for your answer. [2 points]
(c) Find the rate at which the depth is changing when the water is 9 feet deep. Indicate units of measure. [1 point]
(d) Find $h(t)$ , the particular solution to the differential equation with $h(0) = 16$ . At what time is the tank empty? [4 points]

The question