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(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).

Sagot :

MrRoyalidn

Answer:

[tex]A'(t) = rA(t)[/tex]

Step-by-step explanation:

Given

[tex]A(t) \to[/tex] Amount

Required

The differential equation

The equation for the amount is:

[tex]A(t) = A_0 * e^{rt}[/tex]

Where:

[tex]A_0 \to[/tex] initial amount

[tex]r \to[/tex] rate

[tex]t \to[/tex] time

Differentiate[tex]A(t) = A_0 * e^{rt}[/tex]

[tex]A'(t) = A_0 * r * e^{rt}[/tex]

So, we have:

[tex]A'(t) = rA_0 * e^{rt}[/tex]

From the question, we have: [tex]A(t) = A_0 * e^{rt}[/tex]

So, the equation becomes

[tex]A'(t) = rA(t)[/tex]

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