7.5.5-eg-1

# 7.5.5-eg-1 - we have 1600 = 700 e 50 k ln 16 7 = 50 k and...

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Example Suppose the world population in 1750 was 700 million and in 1800, 1600 million. If the world population P in millions as a function of time t in years is modeled by dP dt = kP and the given data are used to predict the world population in 2010, how close is the model’s ﬁgure to the actual population of 6800 million? Given the diﬀerential equation model dP dt = kP we integrate and use as an initial condition P (0) = 700 (the year 1750 to corresponding to time t = 0) to obtain P ( t ) = 700 e kt . 1. Find the growth constant k . Since the population in 1800 (t=50) was 1600 million,
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Unformatted text preview: we have 1600 = 700 e 50 k ln 16 7 = 50 k and so k = ln(16 / 7) 50 . 2. Use the model to determine the answer. Using the exact value of k throughout the remainder of the problem, the model becomes P ( t ) = 700 e ln(16 / 7) 50 t . We use the model and estimate the population in 2010 to be P (260) = 700 e ln(16 / 7) 50 (260) 51524 . 3049 which yields an severe overestimate of the actual population by about 44724 million people....
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## This note was uploaded on 04/02/2012 for the course MTH 132 taught by Professor Kihyunhyun during the Fall '10 term at Michigan State University.

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