Austin qualified for a $30,000 loan with 7.49% interest in order to buy a new ski boat. The term of his loan is 10 years and his
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Answer:
- k ≈ 0.060
- T(4) ≈ 178 °F
Step-by-step explanation:
The desired formula parameters for Newton's Law of Cooling can be found from the given data. Then the completed formula can be used to find the temperature at the specified time.
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<h3>Given:</h3>
k
T(4)
<h3>Solution:</h3>Filling in the given numbers, we have ...
185 = 68 +(208 -68)e^(-k·3)
117/140 = e^(-3k) . . . . . subtract 68, divide by 140
ln(117/140) = -3k . . . . . . take natural logarithms
k = ln(117/140)/-3 ≈ 0.060
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The temperature after 4 minutes is about ...
T(4) = 68 +140e^(-0.060·4) ≈ 68 +140·0.787186
T(4) ≈ 178.205
After 4 minutes, the final temperature is about 178 °F.
