Question

(b) If A(t) is the amount of the investment at time t for the case of continuous compounding, write a differential equation satisfied by A(t).

Answer 1

Answer:

$A'(t) = rA(t)$

Step-by-step explanation:

Given

$A(t) \to$ Amount

Required

The differential equation

The equation for the amount is:

$A(t) = A_0 * e^{rt}$

Where:

$A_0 \to$ initial amount

$r \to$ rate

$t \to$ time

Differentiate$A(t) = A_0 * e^{rt}$

$A'(t) = A_0 * r * e^{rt}$

So, we have:

$A'(t) = rA_0 * e^{rt}$

From the question, we have: $A(t) = A_0 * e^{rt}$

So, the equation becomes

$A'(t) = rA(t)$