The graph of the equation \( A(t) = 3,000(1.14)^t \) represents exponential growth, starting at an initial investment of $3,000 when \( t = 0 \). As \( t \) increases, the value of the investment grows at a consistent rate of 14% per year, illustrating a steep upward trajectory. The key feature is the curvature of the graph, which indicates that as time progresses, the investment's growth accelerates, reflecting the power of compound interest over time. This means that after several years, the investment will yield significantly higher returns due to the accumulating interest.
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 Ais 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. Keep the answer short.
3 answers
Simplify what you just said a little.
The graph of the equation \( A(t) = 3,000(1.14)^t \) shows exponential growth, starting with an initial investment of $3,000. As time increases, the value of the investment rises at a rate of 14% per year. The graph curves upward, indicating that the investment grows faster over time due to compound interest, leading to much higher returns after several years.