1. **State the problem:** We want to find the time $t$ it takes for an initial amount of 7000 to grow to 35000 at an interest rate of 6% compounded continuously. 2. **Formula used:** The formula for continuous compounding is $$A = P e^{rt}$$ where: - $A$ is the amount after time $t$ - $P$ is the principal (initial amount) - $r$ is the annual interest rate (as a decimal) - $t$ is the time in years - $e$ is Euler's number (approximately 2.71828) 3. **Plug in the known values:** $$35000 = 7000 \times e^{0.06t}$$ 4. **Divide both sides by 7000:** $$\frac{35000}{7000} = e^{0.06t}$$ $$5 = e^{0.06t}$$ 5. **Take the natural logarithm (ln) of both sides to solve for $t$:** $$\ln(5) = \ln\left(e^{0.06t}\right)$$ $$\ln(5) = 0.06t$$ 6. **Solve for $t$:** $$t = \frac{\ln(5)}{0.06}$$ 7. **Calculate the value:** $$\ln(5) \approx 1.6094$$ $$t = \frac{1.6094}{0.06} \approx 26.8233$$ 8. **Round to the nearest tenth:** $$t \approx 26.8 \text{ years}$$ **Final answer:** It will take approximately 26.8 years for 7000 to grow to 35000 at 6% compounded continuously.