A graphing calculator may be used for the following problem. t (hours) 0 2 4 6 8 10
S(t)
(⁰C) 142 210 254 280 274 268
The temperature of water in a solar steam power system, for time 0 ≤ ≤ 10, is modeled by the
differentiable function S, where t is measured in hours. Selected values of S(t) are given in the table
above and represent the temperature in degrees Celsius of the water in the solar steam power system.
a) Use the data in the table to evaluate ∫ S′(t)dt. Using correct units, interpret the meaning of ∫ S′(t) over [0,10]dt in the context of this problem.
b) For 0 ≤ t ≤ 6, approximate the average temperature of the water in the system using a right
Riemann approximation. Determine if the approximation is an overestimate or an underestimate.
Justify your answer.
c) For 10 ≤ t ≤ 20 the change in the temperature of the water in the system can be modeled by the
equation S '(t) = –√(2xe)^(√(x^2) – 100x)
. Using this model, determine the total change in the temperature
of the system for the given interval. Interpret your answer in the context of this problem.