11. On a typical day, the snow on a mountain melts at a rate modeled by the function
T πt
sin
6 12
is/hr
A snow maker adds snow at a rate modeled by the
function
+
S(t) = 0.00672 – 0.12t + 0.87.
inlar
Both M and S have units in inches per hour and t
is measured in hours for 0 st 6. At t= 0, the
mountain has 40 inches of snow.
(a) How much snow will melt during the 6-hour
period? Indicate units of measure.
(b) Write an expression for 1(t), the total number of
inches of snow at any time t.
(c) Find the rate of change of the total amount of snow
when t = 3.
(d) For 0 st s 6, at what time t is the amount of snow
a maximum? What is the maximum value? Justify
your answers.
C