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Integral Applications: Snow Accumulation and Removal

APCALC-MDBA8V

One cold morning in Calculus City, the residents wake to 8" of snow on the ground from the night before.

At 7:00 am, the snow starts to fall again at a rate of:

$$S(t)={ t }^{ 2 }+t$$

Rita Rates is excited by the snow, but must get to work!

At 8:00 am, she starts shoveling at a rate $R(t)$ given by:

$$R(t)=3{ t }^{ 3 }$$

How much snow is still on the ground after at 9:00 am when she has to leave?

All rates are measured in inches/hour.

A

$\cfrac { 14 }{ 3 } \text{ inches}$

B

$\cfrac { 3 }{ 4} \text{ inches}$

C

$\cfrac { 2 }{ 3 }\text{ inches}$

D

$\cfrac { 107}{ 12 } \text{ inches}$