Answer
$$\frac{{dy}}{{dx}} = 1.07y$$
Work Step by Step
$$\eqalign{
& y = 5000{e^{1.07x}} \cr
& {\text{Differentiate with respect to }}x \cr
& \frac{{dy}}{{dx}} = \frac{d}{{dx}}\left[ {5000{e^{1.07x}}} \right] \cr
& \frac{{dy}}{{dx}} = 5000\left( {1.07} \right){e^{1.07x}} \cr
& \frac{{dy}}{{dx}} = \left( {1.07} \right)5000{e^{1.07x}} \cr
& {\text{Where }}5000{e^{1.07x}} = y,{\text{ then}} \cr
& \frac{{dy}}{{dx}} = 1.07y \cr
& {\text{The rate of change is proportional to }}y. \cr} $$
