Properties of an Exponential Growth Model

An investment’s value, $V(t)$, is modeled by the function $V(t) = V_0 e^{r*t}$. Consider the following statements: (I) The doubling time for the investment 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 $r*V_0 e^{r*t}$, which implies that the rate of growth is proportional to the current value of the investment. Which of these statements are true?