Answer
$$y = 4{e^{0.8x}}$$
Work Step by Step
$$\eqalign{
& \frac{{dy}}{{dx}} = 0.8y,{\text{ }}y\left( 0 \right) = 4 \cr
& {\text{Separate the variables}} \cr
& \frac{{dy}}{y} = 0.8dx \cr
& {\text{Integrate both sides}} \cr
& \ln \left| y \right| = 0.8x + C \cr
& \ln \left| y \right| = 0.8x + C{\text{ }}\left( {\bf{1}} \right) \cr
& {\text{Use the initial condition }}y\left( 0 \right) = 4 \cr
& \ln \left| 4 \right| = 0.8\left( 0 \right) + C \cr
& C = \ln 4 \cr
& {\text{Substitute }}C{\text{ into }}\left( {\bf{1}} \right) \cr
& \ln \left| y \right| = 0.8x + \ln 4 \cr
& {\text{Solve for }}y \cr
& y = {e^{0.8x + \ln 4}} \cr
& y = 4{e^{0.8x}} \cr
& \cr
& {\text{Graph}} \cr} $$
