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The processing speeds of Peach brand computers is increasing at a rate of r(t) megahertz per year (where t is the time in years). When t=4, the computers had a processing speed of 2500 megahertz. What does 2500+int_(4)^(7)r(t)dt represent? Choose 1 answer: (A) The average rate of change in the processing speed of the computers between t=4 and t=7 (B) The processing speed of the computers when t=7 (C) The net change in processing speeds of the computers between t=4 and t=7 (D) The average processing speed of the computers between t=4 and t=7

The processing speeds of Peach brand computers is increasing at a rate of r(t) r(t) megahertz per year (where t t is the time in years). When t=4 t=4 , the computers had a processing speed of 25002500 megahertz.\newlineWhat does 2500+∫47r(t)dt 2500+\int_{4}^{7} r(t) d t represent?\newlineChoose 11 answer:\newline(A) The average rate of change in the processing speed of the computers between t=4 t=4 and t=7 t=7 \newline(B) The processing speed of the computers when t=7 t=7 \newline(C) The net change in processing speeds of the computers between t=4 t=4 and t=7 t=7 \newline(D) The average processing speed of the computers between t=4 t=4 and t=7 t=7

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Q. The processing speeds of Peach brand computers is increasing at a rate of r(t) r(t) megahertz per year (where t t is the time in years). When t=4 t=4 , the computers had a processing speed of 25002500 megahertz.\newlineWhat does 2500+∫47r(t)dt 2500+\int_{4}^{7} r(t) d t represent?\newlineChoose 11 answer:\newline(A) The average rate of change in the processing speed of the computers between t=4 t=4 and t=7 t=7 \newline(B) The processing speed of the computers when t=7 t=7 \newline(C) The net change in processing speeds of the computers between t=4 t=4 and t=7 t=7 \newline(D) The average processing speed of the computers between t=4 t=4 and t=7 t=7
  1. Understand integral expression: Understand the integral expression.\newlineThe integral ∫47r(t) dt\int_{4}^{7}r(t)\,dt represents the total change in processing speed from time t=4t=4 to t=7t=7. This is because the integral of a rate of change gives the net change over the interval.
  2. Interpret initial value: Interpret the initial value.\newlineThe value 25002500 megahertz is the processing speed at time t=4t=4. This is given in the problem statement.
  3. Combine initial value and integral: Combine the initial value and the integral. Adding the initial processing speed (25002500 megahertz) to the integral of the rate of change (∫47r(t)dt\int_{4}^{7}r(t)dt) gives us the total processing speed at time t=7t=7. This is because we start with the initial speed and add the change in speed over the time interval.
  4. Match expression to correct answer: Match the expression to the correct answer.\newlineThe expression 2500+∫47r(t)dt2500 + \int_{4}^{7}r(t)dt does not represent an average rate of change (A), nor does it represent an average processing speed (D). It represents the processing speed at a specific time (t=7t=7) after accounting for the change from t=4t=4 to t=7t=7, which is the net change in processing speed (C).

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