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.

Answer 1

The equation \( A(t) = 3,000(1.14)^t \) represents exponential growth, indicating that the investment value increases by 14% each year. The initial investment of $3,000 serves as the y-intercept on the graph, where \( t = 0 \). As time progresses, the curve becomes increasingly steep, reflecting the compounding nature of the growth; this means that not only is the initial investment gaining value, but the growth increases over time based on the accumulated value of previous years. After several years, the investment will significantly exceed its original amount, demonstrating the powerful effect of compound interest in long-term investments.

Answer 2

can you write it like a kid

Answer 3

Sure!

The equation \( A(t) = 3,000(1.14)^t \) shows how Andrea's money grows over time. She starts with $3,000, and every year, her money grows by 14%, which means it gets bigger and bigger. At the beginning, the graph starts at $3,000, and as the years go by, it goes up really fast! This means that after a few years, Andrea will have a lot more money because her investment keeps growing quickly. It's like her money is getting a superpower every year!