Calculus Help - Integrals/Constants

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Question Description

A compnay has seen stellar expansion in recent months. The company's profit, P, is currently growing exponentially at 5% each year. The rate of change of the company's profit can be modeled as (1/P)dp=.05dt . Find a general formula that expresses the profit of the company as a function of time, t.

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Explanation & Answer

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integral of (1/P)dp=lnP+C

integral of 0.05dt=0.05t+C

t=(lnP)/0.05, lnP=0.05t, P=e^(0.05t)

thus the profit of the company as a function of time, t, is: P=e^(0.05t)

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Sngva Zraunm (1755)
University of Maryland

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