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

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) $B=500 e^{0.03 t}$