On a typical day, the snow on a mountain melts at a rate modeled by the function M(t) = TU sin it 8 A snow maker adds snow at a rate modeled by the function S(t) = 0.006² - 0.08t + 0.81. Both M and S have units in inches per hour and t is measured in hours for 0 ≤t≤ 4. At t = 0, the mountain has 40 inches of snow. places.) (a) How much snow will melt during the 4 hour period? Indicate units of measure. inches (b) Write an expression for I(t), the total number of inches of snow at any time t. I(t) = (c) Find the rate of change of the total amount of snow when t = 2. inches per hour
On a typical day, the snow on a mountain melts at a rate modeled by the function M(t) = TU sin it 8 A snow maker adds snow at a rate modeled by the function S(t) = 0.006² - 0.08t + 0.81. Both M and S have units in inches per hour and t is measured in hours for 0 ≤t≤ 4. At t = 0, the mountain has 40 inches of snow. places.) (a) How much snow will melt during the 4 hour period? Indicate units of measure. inches (b) Write an expression for I(t), the total number of inches of snow at any time t. I(t) = (c) Find the rate of change of the total amount of snow when t = 2. inches per hour
Chapter3: Polynomial Functions
Section3.5: Mathematical Modeling And Variation
Problem 6ECP: The resistance of a copper wire carrying an electrical current is directly proportional to its...
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Transcribed Image Text:On a typical day, the snow on a mountain melts at a rate modeled by the function.
M(t) = sin
4
A snow maker adds snow at a rate modeled by the function
S(t) = 0.006² - 0.08t+0.81.
Both M and S have units in inches per hour and t is measured in hours for 0 ≤t≤ 4. Att = 0, the mountain has 40 inches of snow. (Round your answers to two decimal
places.)
(a) How much snow will melt during the 4 hour period? Indicate units of measure.
inches ✔
(b) Write an expression for I(t), the total number of inches of snow at any time t.
I(t) =
(c) Find the rate of change of the total amount of snow when t = 2.
inches per hour
(d) For 0 ≤ t ≤ 4, at what time t is the amount of snow a maximum?
hours
What is the maximum value?
inches
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