Water flows into a tank at a rate modeled by liters per minute for

MATHEMATICS · Single correct · AP · Calculus AB · Applications of Integration · Applications of Integration

Problem

Water flows into a tank at a rate modeled by

r(t)=kt^{2}+4

liters per minute for

0\le t\le 5

, where

k

is a constant. If the average inflow rate over this

5

-minute interval is required to be

14

liters per minute, what is the value of

k

? (a)

\dfrac{42}{25}

(b)

\dfrac{6}{5}

(c)

\dfrac{4}{5}

(d)

\dfrac{5}{6}