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. 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 than The amount in the investment continues to over time
The key features of the graph:
1) A(t) at first increases rapidly and then continues to increase over time as t increases. This is because the value of the currency increases at a rate of 14% per year.
2) The y-intercept of the graph is $3,000. This means that when t = 0 (at the start of the investment), the amount in the investment is $3,000.
3) The A-values are greater than $3,000. As t increases, the amount in the investment increases due to the growth rate of 14% per year.
4) The amount in the investment continues to increase indefinitely over time. This is because the growth rate is positive and there is no limit specified in the given equation.
Interpretation of the data:
The equation A(t)= 3,000(1.14)t represents the growth of an investment in an online currency that increases at a rate of 14% per year. The y-intercept of $3,000 indicates the initial investment amount. As time (t) increases, the amount in the investment (A) increases exponentially due to the growth rate. The data suggests that investing in this online currency could lead to significant growth over time.