P28 - change To what special type of point on the graph of...

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Project 28 MAC 2233 1. A population of wolves increases so that the number of wolves x years from now is given by the function W ( x ) = 200(1 - e - x ) . Calculate W 0 ( x ) . At what rate does the population change after 1 year? 3 years? (Include units and round to the nearest tenth). Sketch the graph of W ( x ) for x 0 . Label any asymptotes and intercepts. Evaluate lim x →∞ W ( x ) and lim x →∞ W 0 ( x ) . What is the interpretation of these limits in terms of the wolf population and its growth rate as time passes (to inﬁnity). 2. The function M ( t ) = 100 t 2 e - t ( t 0 ) is a type of function used to measure the level of medication in the bloodstream after a drug administered, where t is measured in minutes and M in milligrams. Make a rough sketch of the graph using its ﬁrst and second derivatives.

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The function above is sometimes called a surge function. Why do you think it is called that based on your graph? After how many minutes is the drug level at a maximum? What is the maximum level? At what times does the medication level experience the maximum and minimum rate of
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Unformatted text preview: change? To what special type of point on the graph of M ( t ) do these correspond? 3. Examine the function g ( t ) = 50 + 30( t-1) 1 3 e-1 6 t . a) Calculate g ( t ) and use a number line to ﬁnd the intervals on which g ( t ) is positive and negative. Find the maximum and minimum value(s) of g ( t ) on [ 0 , 9 ] . b) Suppose g ( t ) represents the temperature (in ◦ F ) of a cold storage room t hours after the room is accidently left open. What is the initial room temperature (to the nearest degree)? What is the maximum room temperature (to the nearest degree), and after how many hours does it occur? c) Suppose the items inside the room must be discarded if they reach a temperature of 70 ◦ F . Should our current room be modiﬁed to safeguard against a total loss in this situation? What happens to the temperature in the long run? (i.e., lim t →∞ g ( t ) )...
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P28 - change To what special type of point on the graph of...

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