MAC3233 Test 4 August 9, 1995 Name Instructions: This is a closed-book, closed-notes test. Do not write your answers on this paper, use separate answer sheets. No calculators are allowed to be used. To receive credit, you must show all work . Some numerical answers may involve the function ln or the number e . 1. (5 points) Let P ( t ) be the number of bacteria present in a culture after t minutes, and suppose that P ( t ) satisﬁes the diﬀerential equation P0 ( t ) = 0 . 35 P ( t ) . Find the formula for P ( t ) if initially there are approximately 13,500 bacteria present. 2. (15 points) Suppose that the velocity of a model car at time t is 1 t + t inches per second where t is in seconds and 1 ≤ t ≤ 10. (a) Find the area under the graph of the velocity curve from t = 1 to t = 10. (b) What does the area in part (a) represent? 3. (15 points) A company can sell q = 400 50 + p 2 refrigerators at a price of p hundred dollars per refrigerator. (a) Find
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