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)', where A is the amount in the investment after t years. Identify
the key features of the graph and interpret the meaning of the data (8 points)
At t increases, A
at first and then
The y-intercept is
than
The A-values are
• thar
The amount in the investment continues to
© over time
The key features of the graph can be identified as follows:
1. As t increases, A also increases. The investment grows over time.
2. At first, the rate of increase is relatively slow. However, as time goes on, the rate of increase becomes higher due to the compounding effect of the 14% annual growth rate.
3. The y-intercept of the graph is $3,000, which represents the initial investment amount.
4. As t increases, A eventually surpasses the initial investment amount of $3,000.
5. The A-values are continuously increasing over time, indicating that the investment is gaining value year after year.
6. The amount in the investment continues to grow exponentially over time due to the compounding effect of the 14% annual growth rate.
In summary, the graph illustrates that Andrea's investment of $3,000 in the online currency grows over time and accumulates more value due to the 14% annual growth rate. The investment initially grows slowly but eventually increases at an increasingly faster rate. The investment eventually surpasses the initial investment amount and continues to grow exponentially over time.