A Sum Of $\$ 2,000$ Is Invested At $20 \%$ Interest If $A ( t )$

Multiple Choice

A sum of $\$ 2,000$ is invested at $20 \%$ 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) $\frac { d A } { d t } = 20 A , \quad A ( 0 ) = 3,000$
B) $\frac { d A } { d t } = 1,500 A , \quad A ( 0 ) = 2,000$
C) $\frac { d A } { d t } = 0.20 A , A ( 0 ) = 200$
D) $\frac { d A } { d t } = 0.20 A ( 0 ) , \quad A ( 0 ) = 2,000$
E) $\frac { d A } { d t } = 0.20 A , \quad A ( 0 ) = 2,000$