Calculus Help - Integrals/Constants

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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.

Jun 13th, 2015

Thank you for the opportunity to help you with your question!

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)

Please let me know if you need any clarification. I'm always happy to answer your questions.
Jun 13th, 2015

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