The equation \( A(t) = 3,000(1.14)^t \) represents an exponential growth model, where the initial investment of $3,000 grows at a rate of 14% per year. The key feature of the graph is its upward exponential curve, indicating that as time \( t \) increases, the amount \( A(t) \) grows more rapidly due to compounding. The graph will pass through the point (0, 3000) when \( t = 0 \) and will continue to rise sharply, reflecting the increasing value of the investment over time. This model demonstrates how the investment grows significantly over the years, highlighting the powerful effect of compound interest in long-term financial planning.
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.
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