A sum of $\$ 5,000$ is invested at $35 \%$ interest. If $A ( t )$ is the amount of the investment at time t for the case of continuous compounding, write a differential equation and an initial condition satisfied by $A ( t )$ .
A) $\frac { d A } { d t } = 4,500 A , \quad A ( 0 ) = 5,000$
B) $\frac { d A } { d t } = 35 A , \quad A ( 0 ) = 3,000$
C) $\frac { d A } { d t } = 0.35 A , \quad A ( 0 ) = 500$
D) $\frac { d A } { d t } = 0.35 A , \quad A ( 0 ) = 5,000$
E) $\frac { d A } { d t } = 0.35 A ( 0 ) , \quad A ( 0 ) = 5,000$

Question

Quizplus · Accepted Answer

Since the investment is continuously compounded at a rate of $35 \% $, the differential equation is given by:
$$\frac { d A } { d t } = r A $$
where $r$ is the interest rate in decimal form. Note that the initial amount invested is given by $A(0) = 5,000$. Therefore, the correct option is $\frac { d A } { d t } = 0.35 A , \quad A ( 0 ) = 5,000$ or option D.

A Sum Of $5,000\$ 5,000$5,000 Is Invested At 35%35 \%35% Interest If A(t)A ( t )A(t)

A Sum Of $\$ 5,000$ Is Invested At $35 \%$ Interest If $A ( t )$