The height of water in a cylindrical tank is measured in centimeters

MATHEMATICS · Single correct · AP · Calculus AB · Contextual Applications of Differentiation · Contextual Applications of Differentiation

Problem

The height

h(t)

of water in a cylindrical tank is measured in centimeters, and

t

is time in seconds. Suppose

h'(5)=0.75

. Which interpretation of this value is most accurate? (a) At

t = 5\text{ s}

, the water level is

0.75\text{ cm}

above the bottom of the tank. (b) At

t = 5\text{ s}

, the water level is increasing at a rate of

0.75\text{ cm/s}

. (c) At

t = 5\text{ s}

, the water level will rise about

0.75\text{ cm}

over the next

1\text{ s}.

(d) At

t = 5\text{ s}

, it will take about

0.75\text{ s}

for the water level to rise

1\text{ cm}