Suppose there is a new kind of savings certificate that starts out paying 1.5% 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.)Which of the following differential equations gives the rate of change in the balance B(t)at time t?
A) $\frac{d B}{d t}=B(0.015+0.01 t)$
B) $\frac{d B}{d t}=B(0.015 t+0.01)$
C) $\frac{d B}{d t}=B(0.025) t$
D) $\frac{d B}{d t}=B(0.025+0.01 t)$

Question

Quizplus · Accepted Answer

The correct differential equation is $\frac{d B}{d t}=B(0.015+0.01 t)$ because it represents a balance that grows at an initial rate of 1.5% annually, with the rate increasing by 1% for each additional year, which matches the description given.

Suppose There Is a New Kind of Savings Certificate That dBdt=B(0.015+0.01t)\frac{d B}{d t}=B(0.015+0.01 t)dtdB​=B(0.015+0.01t)

Suppose There Is a New Kind of Savings Certificate That $\frac{d B}{d t}=B(0.015+0.01 t)$