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AP CALCULUS BC Daija B obe

Integrals, Trapezoidal Rule, and Maximums. 2010 #2. AP CALCULUS BC Daija B obe. The Question.

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AP CALCULUS BC Daija B obe

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  1. Integrals, Trapezoidal Rule, and Maximums. 2010 #2 AP CALCULUS BCDaija Bobe

  2. The Question A zoo sponsored a one-day contest to name a new baby elephant. Zoo visitors deposited entries in a special box between noon (t=0) and 8 P.M. (t=8). The number of entries in the box t hours after noon is modeled by a differentiable function E for 0≤ t ≤8. Values of E(t), in hundreds of entries, at various times t are shown in the table above.

  3. The Question • Use the data in the table to approximate the rate, in hundreds of entries per hours, at which entries were being deposited at time t=6. Show the computations that lead to your answer. • Use a trapezoidal sum with the four subintervals given by the table to approximate the value of Using correct units, explain the meaning of in terms of the number of entries. • At 8P.M., volunteers began to process the entries. They processed the entries at a rate modeled by the function P, where hundreds of entries per hour for 8≤ t ≤ 12. According to the model, how many entries had not yet been processed by midnight (t=12) ? • According to the model from part (c), at what time were the entries being processed most quickly? Justify your answer.

  4. Part A To approximate the rate, in hundreds of entries per hours, at which entries were being deposited at time t=6, you must use the Mean Value Theorem. About 4 hundred entries per hour.

  5. Part B Trapezoidal Rule: Approximately 10. 688 hundreds of entries. is the average number of hundreds of entries in the box between noon and 8P.M.

  6. Part C Given: The number of processed entries The number of unprocessed entries 7 hundred entries haven’t been processed.

  7. Part D The entries are processed the most quickly when P(t) is at maximum. P(t) is at maximum when P’(t)=0. when t=9.183503 and t=10.816497.

  8. Hooray for AP Calculus BC Citation: http://apcentral.collegeboard.com/apc/public/repository/ap10_frq_calculus_bc.pdf

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