Suppose There Is a New Kind of Savings Certificate That $B=500 e^{0.02 t+0.005 t^{2}}$

question 62

Multiple Choice

Suppose there is a new kind of savings certificate that starts out paying 2% annual interest and increases the interest rate by 1% each additional year that the money is left on deposit.(Assume that interest is compounded continuously and that the interest rate increases continuously.) Write a differential equation that gives the rate of change in the balance B(t) at time t, and solve it assuming an initial deposit of $500.What is your equation?

• A) \(B=500 e^{0.02 t+0.005 t^{2}}\)
• B) \(B=500 e^{0.02 t+0.01 t^{2}}\)
• C) \(B=500 e^{0.02+0.01 t}\)
• D) \(B=500 e^{0.03 t}\)

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