Snow accumulates on a driveway according to the piecewise rate r(t)= cases 2+4t, & 0…

MATHEMATICS · Subjective · AP · Calculus AB · Applications of Integration · Applications of Integration

Problem

Snow accumulates on a driveway according to the piecewise rate

r(t)= \begin{cases} 2+4t, & 0\le t\le 2,\\ 10, & t>2, \end{cases}

where

r(t)

is measured in centimeters per hour and

t

is the number of hours since the snowfall began. Find the total time

t

(in hours) required for 50 centimeters of snow to accumulate.