Properties of an Exponential Growth Model
I. The doubling time for an investment growing according to $$V(t) = V_0 e^{r*t}$$ is given by $$t = \frac{\ln(2)}{r}$$.
II. If $$r = 0.07$$, the doubling time is approximately 9.9 years.
III. The derivative of $$V(t)$$ is $$r*V_0 e^{r*t}$$, showing that the growth rate is proportional to the current account balance.
Which of the above statements are true?
TITLE: Investment Account Data: #000000
| Parameter | Value |
|---|---|
| Initial Value | $$V_0$$ |
| Interest Rate | 7% |
| Doubling Time | (to be computed) |
A
I and II only
B
II and III only
C
I, II, and III
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