The amount of money M in an account is increasing at the rate of 9% per year.
(a) Write a differential equation that describes the amount at any time t.
(b) Find the particular solution for M, given that the account begins with $2,000 in it.
(c) When will there be $24,000 in the account?
a) dM/dt = 0.09M
b) dM/dt = 0.09M
dM/M = 0.09 dt
Upon integration, we get ln M = 0.09t + ...
A complete, step-by-step solution is provided.