In a certain city the temperature (in °F) t hours after 9 AM was modeled by the function T(t) = 58 − 2.4t + 0.43t2 − 0.018t3. Find the average temperature during the period from 9 AM to 9 PM.

Question

Round your answer to one decimal place.)

Answer 1

Since this question has been submitted under Calculus Answers, here is the calculus answer:

To take an average you sum the data and divide by the size of the data: ∑T/n. So we would have (T₁+T₂+T₃+...)/n. In calculus ∑ is replaced by ∫ so we have ∫Tdx in the interval [0,12] because there are 12 hours between 9am and 9pm. Applying this we get [58t-1.2t²+0.43t³/3-0.018t⁴/4] in [0,12].

This gives us 677.568 as the “sum” and we divide this by 12 to get the average: 56.464℉. Round this to 1 place of decimals: 56.5℉.