A continuous function models the ambient outdoor temperature (in °F) over a 24-hour…
MATHEMATICS · Multi-part · AP · Calculus AB · Applications of Integration · Applications of Integration
Problem
A continuous function T models the ambient outdoor temperature (in °F) over a 24-hour period from midnight (t=0 h) to the following midnight (t=24 h). A meteorologist records the temperatures every 3 hours, obtaining the values shown below. Between successive data points, the graph of T is assumed to be piecewise linear.
Time t (h): 0 3 6 9 12 15 18 21 24
Temperature T(t) (°F): 62 60 58 61 67 72 70 66 63
Answer the following questions about the average temperature during the 24-hour period.
(a) Describe, without performing any calculation, how the average temperature over the interval 0≤t≤24 is related to the area under the temperature–time curve.
(b) Explain why, based solely on the tabulated data, the average temperature must lie between 58 °F and 72 °F.
(c) Discuss one limitation of using the piecewise-linear approximation described above for estimating the average temperature.