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

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) $\frac { d A } { d t } = 0.35 A ( 0 ) , \quad A ( 0 ) = 5,000$

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