t4(2)

# t4(2) - (1-10 x 5 dx 5(15 points A local tool and die...

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Methods of Calculus MAC3233 Make-up Test 4 December 5, 1994 Name Instructions: Do not write your answers on this paper, use separate answer sheets. This is a closed-book test. No calculators are allowed to be used. Do not simplify your answers. 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 P 0 ( t ) = 0 . 53 P ( t ) . Find the formula for P ( t ) if initially there are approximately 10,000 bac- teria present. 2. (15 points) Write the equation of the tangent line to the graph of y = 2ln( x ) x at x = 1. 3. (15 points) A company can sell q = 400 p 127 - p refrigerators at a price of p hundred dollars per refrigerator. (a) Find E ( p ), the elasticity of demand. (b) Find E (6). Is demand elastic, or inelastic at p = 6? (c) If the current price is p = 6, will revenue increase or decrease if p is raised slightly? 4. (10 points each) Find the following antiderivatives. (a) Z 15 e 2 x dx (b) Z 3 x + 5 dx (c) Z 5 - 1

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Unformatted text preview: (1-10 x 5 ) dx 5. (15 points) A local tool and die company wants to know how much it costs to keep a machine running in their shop. Taken into consideration are all expenses associated to owning and operating the machine, including de-preciation due to wear and tear and necessary maintenance costs. Suppose that for a machine which has been in service for t months, expenses cost the company a rate of t 2-24 t + 250 dollars per month. If a machine has been in service for 12 months, ﬁnd the total expenses of keeping it running for an additional 18 months. 6. (20 points) For the curves y = x 2-2 x + 1 and y = 13-x 2 answer the following. 1 (a) Sketch the graphs of the curves (on the same coordinate plane). (b) Find the x-coordinates of the points where the curves intersect. (c) Find the area of the region bounded by the curves. 2...
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t4(2) - (1-10 x 5 dx 5(15 points A local tool and die...

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