Question

Andrea invested $3,000 in an online currency. If the value of the currency increases at a rate of 14% per year, the situation can be modeled using the equation A(t)=3,000(1.14)t
, where A
is the amount in the investment after t years. In 3–5 sentences, identify the key features of the graph and interpret the meaning of the data.

Answer 1

The graph is an exponential growth curve with y‑intercept A(0) = $3,000 (the initial investment) and growth factor 1.14, so it rises steadily and steepens over time. The investment increases by 14% each year — for example A(1) = $3,000(1.14) = $3,420 — and is multiplied by 1.14 for every additional year. Domain is t ≥ 0 and range is A ≥ $3,000; there are no x‑intercepts and A(t) → ∞ as t → ∞. Using the rule of 70 gives a rough doubling time of 5 years; a more precise calculation gives about 5.3 years for the investment to reach $6,000.