Question

Luna tracks her finances using a budgeting app. The app tells her that if she leaves the money in her savings account alone, the amount of money in the account after t years will be 400(1.06)t dollars.
How does the money in the account change over time?

Answer 1

The amount grows exponentially. It starts at $400 (when t = 0) and increases by 6% each year, so after t years the balance is
400(1.06)^t dollars.
Examples: after 1 year $=400(1.06)=\$424$, after 2 years $=400(1.06)^2\approx\$449.44$. The balance roughly doubles in about ln(2)/ln(1.06) ≈ 11.9 years.