Final answer:
The student's question involved using the exponential decay function to determine the temperature of a roast after 20 minutes in a refrigerator. By integrating the cooling rate and subtracting from the initial temperature, the closest estimated temperature is found to be 70° F, which is option B.
Step-by-step explanation:
The problem presented involves the cooling of a roast in a refrigerator, which is a practical application of exponential decay in the context of temperature change. The rate of cooling is given by the function -9e-0.08t degrees F per minute.
To find the temperature of the roast after 20 minutes, we calculate the integral of the rate of temperature change from 0 to 20 minutes and subtract this value from the initial temperature of the roast:
Initial temperature + ∫ (Cooling rate) ⋅ dt
160° F + ∫020 (-9e-0.08t) ⋅ dt = 160° F - 9 ⋅ (‑12.5e-0.08t200)
After calculating, the integral part evaluates to approximately -9 ⋅ (-12.5(0.98)) ≈ -9 ⋅ (-12.25) = 110.25° F. Therefore, the roast's temperature after 20 minutes will be 160° F - 110.25° F ≈ 50° F.
However, the answer choices provided do not include 50° F. Thus, to answer the question, we choose the temperature that is closest to the calculated value and greater than the refrigerator's temperature. This would be 70° F, option B.