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Answer :
Final answer:
The temperature of the potato when first placed in the oven is 10°C. After 30 minutes, its temperature rises to approximately 35.2°C. The potato reaches a temperature of 40°C at around 53 minutes.
Explanation:
The temperature of the potato at the moment it is placed in the oven is determined by substituting t=0 into the equation, yielding p(0) = 200 - 190(0.97^0), which simplifies to 200 - 190 = 10°C. Half an hour after it has been placed in the oven, or t=30 minutes, we substitute into the equation to find p(30) = 200 - 190(0.97^30), which rounds to 35.2°C. Finally, when the potato is 40°C, we set the equation equal to 40 and solve for t to get k = log(160/190) / log(0.97), which is approximately 53 minutes.
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