# P31 - Write the particular function having derivative F x...

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Project 31 MAC 2233 1. Recall the formula and graph for the logistic function; note that one example is the function P ( t ) = 100 1 + 2 e - 0 . 2 t . Where does the inflection point for the graph occur? Now sketch the function P ( t ) on the axes above. Include the intercept, inflection point, and asymptote. Suppose the function P ( t ) represents the population of whales in a certain area t years from now. What is the population of whales now? When will the population be 75 whales? To what number will the population tend in the long run? 2. Examine the function f ( x ) = x 2 - x + 2 x on ( 0 , ) . Find any one antiderivative for f ( x ) . What is the general antiderivative for f ( x ) ? Calculate the indefinite integral Z f ( x ) d

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Unformatted text preview: . Write the particular function having derivative F ( x ) on the interval (0 , ∞ ) and passing through the point (1 , 10) . What is the value of F ( x ) when x = 2 ? 3. Show that F ( t ) = 2 5 (9-t ) 5 2-6(9-t ) 3 2 is an antiderivative for the function f ( t ) = t √ 9-t on [0 , 9) . Suppose that at any time t ≥ (in hours) the rate at which water ﬂows into a tank (in liters per hour) is given by the formula 10 + 5 f ( t ) . Find the formula V ( t ) for the volume of water in the tank at time t if the tank is initially empty (at t = 0 ). Find the volume of water in the tank after 9 hours....
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