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P18Ans - Project 17/18 MAC 2233 1 The idea of a...

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Project 17/18 MAC 2233 1. The idea of a differential is pretty simple if you can get past the notation. Consider the fol- lowing problem: Suppose the value (in dollars) of some electronic equipment t years from now is given by V ( t ) = 400 + 1600 1 + t 2 . Find the value of the equipment 1 year from now, and the rate at which the value of the equipment is changing with respect to time 1 year from now. Include units (very important for the next question). 1200 dollars; - $ 800 per year Based only on common sense and your answers to the previous two questions, explain what you would guess to be the value of the equipment 1 1 4 years from now. (Don’t plug in. . . guess!) 1000 dollars You just used differentials. Let’s show it. . . Start by calculating the formula for the differential dV . What quantity does it approximate? d V = - 3200 t (1 + t 2 ) 2 d t per year To approximate the change in value V from year 1 to year 1 1 4 , what would be the values of t and dt that you should put into the differential dV ? Evaluate the differential with these values.
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