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Calculating Total Pollutant Exposure

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The concentration of a pollutant is modeled by the function C(t)=5+0.5tC(t) = 5 + 0.5t, where C(t)C(t) is the concentration in parts per million (ppm) and tt is the time in hours. Calculate the total pollutant exposure in ppm·hours over the first 8 hours by evaluating the definite integral of C(t)C(t) from t=0t=0 to t=8t=8.

A

48 ppm·hours

B

72 ppm·hours

C

56 ppm·hours

D

64 ppm·hours, a value likely arising from an overestimate of the area under the curve due to miscalculation of the integral.

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