Question 1110282: Hello, I would like some help solving this word problem!
The level of air pollution varies throughout the day during summer. The function P(t)= 0.1t^2-0.4t+0.6 measures the air pollution, "P" measured in parts per million, with respect to time, "t" in hours, where 9AM=0
A) Find the average rate of change of air pollution between noon and 5PM.
B) Find the rate of change at 5PM and interpret the meaning of your result.
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Hello, I would like some help solving this word problem!
The level of air pollution varies throughout the day during summer. The function P(t)= 0.1t^2-0.4t+0.6 measures the air pollution, "P" measured in parts per million, with respect to time, "t" in hours, where 9AM=0
A) Find the average rate of change of air pollution between noon and 5PM.
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Average = [P(5)-P(0)]/[5-0] = [0.1*25-0.4*5+0.6 - (0-0+0.6)]/5 = 0.1
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B) Find the rate of change at 5PM and interpret the meaning of your result.
P'(t) = 2*0.1t-0.4
P'(5) = 2*0.1*5-0.4 = 0.6
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Cheers,
Stan H.
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