Chapter 5.2, Problem 25E

Differential Equation and InterestA small amount of money is deposited in a savings account with interest compounded continuously. Let $A\left(t\right)$ be the balance in the account after $t$ years. Match each of the following answers with its corresponding question.

Answers

a. $P{e}^{rt}$

b. $A\left(3\right)$

c. $A\left(0\right)$

d. $A\text{'}\left(3\right)$

e. Solve $A\text{'}\left(t\right)=3$ for $t$.

f. Solve $A\left(t\right)=3$ for $t$.

g. $y\text{'}=ry$

h. Solve $A\left(t\right)=3A\left(0\right)$ for $t$.

Questions:

A. How fast will the balance be growing in $3$ years?

B. Give the general form of the function $A\left(t\right)$.

C. How long will it take for the initial deposit to triple?

D. Find the balance after $3$ years?

E. When will the balance be $3$ dollars?

F. When will the balance be growing at the rate of $3$ dollars per year ?

G. What was the principal amount?

H. Give a differential equation satisfied by $A\left(t\right)$.