Question

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.

Answer 1

[AI-generated answer — Bot GPT 3.5]

The key features of the graph of the equation A(t) = 3,000(1.14)^t are:

1. Initial investment: The initial amount invested is $3,000. This is represented by the starting point on the graph at t = 0.

2. Growth rate: The online currency increases in value at a rate of 14% per year. This growth rate is represented by the factor 1.14 in the equation.

3. Exponential growth: The equation represents exponential growth because the value of the investment is multiplied by the growth rate (1.14) raised to the power of time (t).

4. Tendency towards infinity: As the time (t) increases, the value A(t) of the investment increases exponentially. However, it will never reach a finite maximum value since it is an exponential growth model.

Interpretation of the data:

The equation A(t) = 3,000(1.14)^t represents the increasing value of the investment over time. For example, after 1 year (t = 1), the investment is worth $3,420 (3,000 * 1.14). After 2 years (t = 2), the investment is worth $3,896.80 (3,420 * 1.14), and so on.

This means that the investment grows at a rate of 14% per year, compounding annually. The larger the value of t, the greater the growth of the investment. Over a longer period of time, the investment will continue to increase rapidly. However, it is important to note that exponential growth models like this can have risks and are subject to market fluctuations, so real-world results may vary.