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%0D%0A%0D%0A(%0D%0A%0D%0A)%0D%0A=%0D%0A %0D%0A3%0D%0A,%0D%0A000%0D%0A(%0D%0A1.14%0D%0A)%0D%0A%0D%0A , 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
The key features of the graph can be identified by analyzing the equation A(t) = 3,000(1.14)t.
1. Initial investment: The initial investment amount is $3,000. This is the starting point on the graph.
2. Exponential growth: The equation implies exponential growth as it is in the form of A(t) = a(1+r)^t, where a is the initial amount, r is the growth rate, and t is the time in years. In this case, the growth rate is 14% per year.
3. Growth factor: The growth factor in this equation is (1.14), which represents an increase of 14% per year.
4. Time: The variable t represents the number of years. As t increases, the value of the investment grows.
Interpretation of the data:
The equation shows that Andrea's investment will increase exponentially over time at a rate of 14% per year. This means that for each year that passes, the investment will grow by 14% of its current value. The graph would show a steeply increasing curve, indicating rapid growth.
For example, after 1 year, the investment will be 3,000(1.14) = $3,420. After 2 years, it will be 3,420(1.14) = $3,896.80. This pattern continues, with the investment value growing significantly over time.
Overall, the equation and graph illustrate the potential for substantial growth in Andrea's investment over the years, thanks to the compounded effect of the 14% annual increase.