Explain properties of logarithms and exponential functions

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Reference no: EM131798674

Question: Investment when the interest on an investment is compounded continuously, the investment grows at a rate that is proportional to the amount in the account, so that if the amount present is P, then

dP/dt = kP

where P is in dollars, t is in years, and k is a constant.

(a) Solve this differential equation to find the relationship.

(b) Use properties of logarithms and exponential functions to write P as a function of t.

(c) If $50,000 is invested (when t = 0) and the amount in the account after 10 years is $135,914, find the function that gives the value of the investment as a function of t.

(d) In part (c), what does the value of k represent?

Reference no: EM131798674

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