Answer
$$\eqalign{
& {\text{Annual rate: }}4\% \cr
& {\text{Time to double: }}17.33{\text{ years}} \cr} $$
Work Step by Step
$$\eqalign{
& {\text{Initial Investment: \$ 6000}} \to {A_0} = {\text{\$ 6000}} \cr
& {\text{For }}t = 10 \to A = \$ 8950.95 \cr
& A = {A_0}{e^{rt}}{\text{, }}t{\text{ in years}} \cr
& {\text{Therefore,}} \cr
& \$ 8950.95 = \$ {\text{6000}}{e^{r\left( {10} \right)}} \cr
& {\text{Solve for }}r \cr
& {e^{10r}} = \frac{{8950.95}}{{{\text{6000}}}} \cr
& 10r = \ln \left( {\frac{{8950.95}}{{{\text{6000}}}}} \right) \cr
& r = \frac{1}{{10}}\ln \left( {\frac{{8950.95}}{{{\text{6000}}}}} \right) \cr
& r = 0.04 \cr
& r = 4\% \cr
& \cr
& A = {A_0}{e^{rt}} \to A = 6000{e^{0.04t}} \cr
& {\text{The time to double is }}A = 2{A_0} \cr
& 12000 = 6000{e^{0.04t}} \cr
& t = \frac{{\ln 2}}{{0.04}} \cr
& t = 17.3286 \cr
& t \approx 17.33{\text{ years}} \cr} $$
