The graph of the equation \( A(t) = 3,000(1.14)^t \) is an exponential curve that starts at the point (0, 3000), representing the initial investment of $3,000. As time (t) increases, the amount in the investment grows rapidly due to the constant annual growth rate of 14%, illustrating the effect of compound interest. The steepness of the curve increases as time progresses, highlighting that the investment grows faster as it accumulates more interest on top of the increasing principal. This model shows that over time, even a modest initial investment can lead to significant financial growth due to the power of compounding.
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
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)
1 answer
1 answer