Water flows into and out of a reservoir at a rate (in liters per minute) for

MATHEMATICS · Single correct · AP · Calculus AB · Integration and Accumulation of Change · Integration and Accumulation of Change

Problem

Water flows into and out of a reservoir at a rate

r(t)

(in liters per minute) for

t>0

. The volume of water in the reservoir at time

t

R(t)=\int_{0}^{t} r(s)\,ds

. Suppose

r(t)>0

for

0<t<6

r(t)<0

for

6<t<9

, and

r(t)>0

for

t>9

. Which of the following best describes the behavior of

R

? (a)

R

increases on

(0,6)

, increases on

(6,9)

, and increases on

(9,\infty)

. (b)

R

increases on

(0,6)

, increases on

(6,9)

, and decreases on

(9,\infty)

. (c)

R

increases on

(0,6)

, decreases on

(6,9)

, and increases on

(9,\infty)

. (d)

R

increases on

(0,6)

, decreases on

(6,9)

, and decreases on

(9,\infty)