24Solving exponential growth

An account holds $\displaystyle A = 500e^{0.04t}$ dollars after $\displaystyle t$ years. When does it reach 800 dollars? Give the answer to 3 decimal places.

The balance hits $800 at t ≈ 11.750 years. Dividing 800 by 500 gives e^(0.04t) = 1.6, and taking ln of both sides gives t = ln(1.6)/0.04 ≈ 11.750. Checking: 500e^(0.04·11.750) ≈ 500(1.6) = 800.