4_04-1

4_04-1 - FnInt(3 2cos(2pit/15,x,0,t t>0 since integral...

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This is an example of a Calculator Active question similar to what can be expected on the AP Exam. Set-up for the solution should be shown, and you must use correct notation but you do not have to show your calculations. Pumping stations deliver raw waste to a dump site at the rate modeled by the function D, given by 10t D(t) 1 2t = + Cleaning pumps remove the waste at a rate modeled by the function R, given by 2 t R(t) 3 2cos 15 π = + Both D(t) and R(t) have units of tons per hour and t is measured in hours for 0 t 8 . At time t = 0, the dump site contains 3000 tons of waste. a. Write the integral expression for the amount of waste that the pumping stations will deliver from time t = 0 to time t. FnInt(10t/(1+2t),x,0,t) t>0, since integral from 0 to 0=0 b. How much waste will the pumping stations deliver to the site during this 8 hour period? Give 3 decimal places and indicate units of measure. FnInt(10t/(1+2t),x,0,8)

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c. Write the integral expression for the amount of waste that the cleaning pumps will remove from time t = 0 to time t.
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Unformatted text preview: FnInt(3+2cos (2pit/15),x,0,t) t>0, since integral from 0 to 0=0 d. How much waste will the cleaning pumps remove from the site during this 8 hour period? Give 3 decimal places and indicate units of measure. FnInt(3+2cos (2pit/15),x,0,8) e. Write an expression for W(t), the total number of tons of waste in the site at time t. Integral of D(t) – Integral R(t)=W(t) f. What is the amount of waste at the site at time t = 8? Give 3 decimal places and indicate units of measure. FnInt(10t/(1+2t),x,0,8)-FnInt(3+2cos (2pit/15),x,0,8) g. Write an expression for W’(t), the rate of change of the total amount of waste at the site at time t. h. Find a critical value for W(t) in the interval 0 < t < 8. Give 3 decimal places and explain what this critical value means to the amount of waste in the dump at this time. i. For t 8 h& , at which time t is the amount of waste in the site a minimum? What is this minimum value? Justify your answer....
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This note was uploaded on 05/15/2011 for the course ECON 101 taught by Professor Dannicatambay during the Fall '08 term at UPenn.

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4_04-1 - FnInt(3 2cos(2pit/15,x,0,t t>0 since integral...

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