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The function b(t) gives the temperature (in degrees Celsius) of a pan of brownies by time t (in minutes). What does int_(0)^(6)b^(')(t)dt=93 mean? Choose 1 answer: (A) At t=6 minutes, the temperature of the brownies is 93 degrees Celsius. (B) The temperature of the brownies increased by 93 degrees Celsius in the first six minutes. (C) During the first six minutes, the temperature of the brownies increases an average of 93 degrees Celsius per minute. (D) At t=6 minutes, the brownies have an instantaneous rate of temperature change of 93 degrees Celsius per minute.

The function b(t) b(t) gives the temperature (in degrees Celsius) of a pan of brownies by time t t (in minutes).\newlineWhat does ∫06b′(t)dt=93 \int_{0}^{6} b^{\prime}(t) d t=93 mean?\newlineChoose 11 answer:\newline(A) At t=6 t=6 minutes, the temperature of the brownies is 9393 degrees Celsius.\newline(B) The temperature of the brownies increased by 9393 degrees Celsius in the first six minutes.\newline(C) During the first six minutes, the temperature of the brownies increases an average of 9393 degrees Celsius per minute.\newline(D) At t=6 t=6 minutes, the brownies have an instantaneous rate of temperature change of 9393 degrees Celsius per minute.

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Q. The function b(t) b(t) gives the temperature (in degrees Celsius) of a pan of brownies by time t t (in minutes).\newlineWhat does ∫06b′(t)dt=93 \int_{0}^{6} b^{\prime}(t) d t=93 mean?\newlineChoose 11 answer:\newline(A) At t=6 t=6 minutes, the temperature of the brownies is 9393 degrees Celsius.\newline(B) The temperature of the brownies increased by 9393 degrees Celsius in the first six minutes.\newline(C) During the first six minutes, the temperature of the brownies increases an average of 9393 degrees Celsius per minute.\newline(D) At t=6 t=6 minutes, the brownies have an instantaneous rate of temperature change of 9393 degrees Celsius per minute.
  1. Understand Meaning: Understand the meaning of the integral of a derivative function. The integral of a derivative function b′(t)b'(t) over an interval [0,6][0, 6] represents the net change in the function b(t)b(t) over that interval. In this context, b(t)b(t) represents the temperature of the brownies, and b′(t)b'(t) represents the rate of change of the temperature with respect to time. The integral of b′(t)b'(t) from 00 to 66 being equal to 9393 means that the net change in temperature from time t=0t=0 to [0,6][0, 6]00 minutes is 9393 degrees Celsius.
  2. Interpret Choices: Interpret the given answer choices in the context of the integral.\newline(A) This choice suggests that the temperature at a specific time is 9393 degrees Celsius, which is not what the integral of a rate of change represents.\newline(B) This choice suggests that the temperature increased by a total of 9393 degrees Celsius over the first six minutes, which aligns with the meaning of the integral of the rate of change.\newline(C) This choice suggests an average rate of change per minute, which is not directly related to the integral of the rate of change over a time period.\newline(D) This choice suggests an instantaneous rate of change at a specific time, which is not what the integral represents; it represents the total change over an interval.
  3. Choose Correct Answer: Choose the correct answer based on the interpretation of the integral. The correct interpretation of the integral from 00 to 66 of b′(t)extdtb'(t) ext{ dt} equal to 9393 is that the temperature of the brownies increased by a total of 9393 degrees Celsius over the first six minutes. Therefore, the correct answer is (B)(B).

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