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

Question

Quizplus · Accepted Answer

The differential equation for the balance B(t) with continuously compounded interest that increases over time is given by $\frac{dB}{dt} = B(t) \cdot (0.02 + 0.01t)$. Solving this differential equation with the initial condition B(0) = 500 leads to the solution $B=500 e^{0.02 t+0.005 t^{2}}$.

Suppose There Is a New Kind of Savings Certificate That B=500e0.02t+0.005t2B=500 e^{0.02 t+0.005 t^{2}}B=500e0.02t+0.005t2

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