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Differential equation, Particular solution

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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?

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Solution Preview

a) dM/dt = 0.09M

b) dM/dt = 0.09M

dM/M = 0.09 dt

Upon integration, we get ln M = 0.09t + ...

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