An investment account, which earns interest and has regular deposits, can be modeled by the initial value problem B '(t) aB m for t 0, with B(0) B 0 The constant a reflects the monthly interest rate, m is the rate of monthly deposits, and B 0 is the initial balance in the account Solve the initial ...

An investment account, which earns interest and has regular deposits, can be modeled by the initial value

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An investment account, which earns interest and has regular deposits, can be modeled by the initial value problem B'(t) = aB + m for t ≥ 0, with B(0) = B₀. The constant a reflects the monthly interest rate, m is the rate of monthly deposits, and B₀ is the initial balance in the account. Solve the initial value problem with a = 0.005, m = $100/month, and B₀ = $100. After how many months does the account have a balance of $7500?

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