Suppose a roast, initially at 60°F is placed in a 350°F oven at 11 AM. The temperature of the roast is measured every 15 minutes for the first hour, with the following results.
Time | 11 AM | 11:15 AM | 11:30 AM | 11:45 AM | 12 noon |
Temperature (°F) | 50 | 67 | 82 | 96 | 110 |
Assuming that u(t) = 350 – T(t) is an exponentially declining function, find the best fit of the form T(t) = 350 – a • e–kt. When will the roast be 200°F, and hence ready to serve (medium)?
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