Invest $5000 compound interest continuously and earns 6% how long till it doubles

1. Continuous compound interest formula:
A = P e^{rt}
2. Set \( A \) to \( 2P \):
2P = P e^{rt}
3. Divide both sides by \( P \):
2 = e^{0.06t}
4. Take the natural logarithm on both sides:
\ln(2) = \ln(e^{0.06t})
5. Simplifying \( \ln(e^{0.06t}) \):
\ln(2) = 0.06t
6. Solving for \( t \):
t = \frac{\ln(2)}{0.06}
t = \frac{0.6931}{0.06}
t \approx 11.552
7. Answer:
t \approx 11.552 \text{ years}