The graph of the equation \( A(t) = 3,000(1.14)^t \) represents exponential growth, where the investment amount increases over time as the currency value rises at a constant rate of 14% per year. The initial value of the investment is $3,000, which is the y-intercept of the graph. As time \( t \) increases, the value of \( A(t) \) rises steeply, demonstrating the compounding effect of the growth rate. By interpreting the model, we can see that after each year, the value of the investment not only increases by a percentage of the initial amount but also accumulates on the increased amount from the previous year, illustrating the nature of exponential growth in investments.
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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