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AP CALCULUS BC 2009 FORM B FRQ QUESTION #2

AP CALCULUS BC 2009 FORM B FRQ QUESTION #2. Dong Yi Chen. Tasks. Solve the problem : Graphically Verbally Algebraically Numerically.

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AP CALCULUS BC 2009 FORM B FRQ QUESTION #2

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  1. AP CALCULUS BC 2009 FORM B FRQ QUESTION #2 Dong Yi Chen

  2. Tasks • Solve the problem : • Graphically • Verbally • Algebraically • Numerically

  3. A storm washed away sand from a beach, causing the edge of the water to get closer to a nearby road. The rate at which the distance between the road and the edge of the water was changing during the storm is modeled by f(t) = t + cos t – 3 meters per hour, t hours after the storm began.

  4. The edge of the water was 35 meters from the road when the storm began, and the storm lasted 5 hours. The derivative of f (t) is

  5. PART A What was the distance between the road and the edge of the water at the end of the storm?

  6. Solution (Graphically) • Looking at the graph, find the area under the curve in order to find the distance

  7. Solution (Graphically)

  8. PART B Using correct units, interpret the value f ‘(4) = 1.007 in terms of the distance between the road and the edge of the water.

  9. Solution (Verbally) At 4 hours into the thunderstorm, the rate at which the distance between the road and the edge of the water was changing and is increasing by 1.007 meter/ hour square

  10. PART C At what time during the 5 hours of the storm was the distance between the road and the edge of the water decreasing most rapidly? Justify your answer.

  11. Solution (Algebraically)

  12. PART D Write an equation involving an integral expression whose solution would give the number of days that sand must be pumped to restore the original distance between the road and the edge of the water.

  13. Solution (Numerically)

  14. Citation "2009 Calculus BC Form B." AP Calculus Form B Questions. College Board, n.d. Web. 20 May 2013.<http://apcentral.collegeboard.com/apc/public/repository/ap09_calculus_bc_form_b_sgs.pdf>.

  15. Thank You!!!!!

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