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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 processing speed of the computers when t=7 (B) The average processing speed of the computers between t=4 and t=7 (C) The net change in processing speeds of the computers between t=4 and t=7 (D) The average rate of change in the 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 processing speed of the computers when t=7 t=7 \newline(B) The average processing speed of the computers between t=4 t=4 and 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 rate of change in the 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 processing speed of the computers when t=7 t=7 \newline(B) The average processing speed of the computers between t=4 t=4 and 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 rate of change in the 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 rate of change of processing speed is given by r(t)r(t), and integrating this rate over a period of time gives the total change in processing speed over that time period.
  2. Interpret initial value: Interpret the initial value. The value 25002500 megahertz is the processing speed of the computers at time t=4t=4. This is the starting point before we add the change in processing speed that occurs from t=4t=4 to t=7t=7.
  3. Combine initial value and change: Combine the initial value and the change. The expression 2500+∫47r(t)dt2500 + \int_{4}^{7}r(t)dt combines the initial processing speed at t=4t=4 with the total change in processing speed from t=4t=4 to t=7t=7. This results in the processing speed of the computers at time t=7t=7.
  4. Match expression to correct choice: Match the expression to the correct choice.\newlineSince we have determined that the expression represents the initial processing speed plus the change in processing speed up to time t=7t=7, the correct choice is:\newline(A) The processing speed of the computers when t=7t=7.

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