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

Question

𝐴
(
𝑡
)
=
3
,
000
(
1.14
)
𝑡
, where A
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.(2 points)

Answer 1

The equation \( A(t) = 3,000(1.14)^t \) represents exponential growth, indicating that the investment increases at a rate of 14% per year. Key features of the graph include the y-intercept at \( A(0) = 3,000 \), which represents the initial investment, and the upward-sloping curve that becomes steeper over time due to the compounding effect of the interest rate. As \( t \) increases, the value of \( A(t) \) rises significantly, illustrating the potential for wealth accumulation over multiple years. This model suggests that the longer Andrea keeps the investment, the more substantial the returns will be, emphasizing the importance of time in growing investments through compounding.