Answer
$$\eqalign{
& {\text{Time to double: }}11.55{\text{ years}} \cr
& {\text{Amount after 10 years: }}\$ 7288.48 \cr} $$
Work Step by Step
$$\eqalign{
& {\text{Initial Investment: \$ 4000}} \to {A_0} = 4000 \cr
& {\text{Annual Rate: 6% }} \to r = 0.06 \cr
& A = {A_0}{e^{rt}}{\text{ }}\left( {\bf{1}} \right){\text{, }}t{\text{ in years}} \cr
& {\text{The time to double is }}A = 2{A_0} \cr
& A = 2\left( {4000} \right) \cr
& A = 8000 \cr
& {\text{Substituting known values into }}\left( {\bf{1}} \right) \cr
& 8000 = 4000{e^{0.06t}} \cr
& {e^{0.06t}} = 2 \cr
& \ln {e^{0.06t}} = \ln 2 \cr
& 0.06t = \ln 2 \cr
& t = \frac{{\ln 2}}{{0.06}} \cr
& t = 11.55{\text{ years}} \cr
& \cr
& {\text{*The amount after 10 years is:}} \cr
& A = {A_0}{e^{rt}} \cr
& A = \$ 4000{e^{0.06\left( {10} \right)}} \cr
& A = \$ 7288.48 \cr} $$
