Question

Read the following scenario, and then answer the question.

Juan assumes that the temperature of the hot tea cooling on his desk can be modeled with an exponential function like this one: T(t)=179(0.92)t. He bases his assumption on the following: The tea cools about 8% every minute. The tea's current temperature is around 179 degrees Fahrenheit.

Which explanation correctly addresses Juan's assumption?

He is incorrect. The tea will cool linearly since it cools at the same number of degrees every minute.
He is correct. The tea will cool exponentially since it cools at a percentage rate every minute.
He is incorrect. The tea will cool along the curve of a parabola since it cools at an increasing percentage rate every minute.

Answer 1

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Answer:

(b) He is correct. The tea will cool exponentially since it cools at a percentage rate every minute.

Explanation:

Newton's Law of Cooling says the change in temperature is proportional to the temperature. This relation gives rise to an exponential function describing the temperature.

In this description, the temperature referred to is the difference between the temperature of the object and the temperature of the environment to/from which heat is being transferred.

Juan is only partially correct. The function is exponential, but the temperature that should be used in his equation is not the temperature of the tea, but the temperature difference between the tea and his desk.

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The curve is not linear and not parabolic, excluding the other answer choices.