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.
If $100,000 is invested (when t0) and the amount in the account after 15 years is $211,700, find the function that gives the value of the investment as a function of t. What is the interest rate on this investment?