(a) Which curve fits the data best?

The curve in Figure 2 fits the data best. The points align closely with the exponential curve $y = 583(1.05)^x$, while the curves in Figure 1 and Figure 3 show significant deviation from the data points.

(b) Using the equation $y = 583(1.05)^x$ to predict the amount after 31 years:

The equation is: $y = 583(1.05)^x$ Substitute $x = 31$: $y = 583(1.05)^{31}$

Let me calculate the value. Given values initial_amount = 583 growth_rate = 1.05 time = 31

Calculate the amount using the exponential formula

amount = initial_amount * (growth_rate ** time) amountThe predicted amount after 31 years is approximately $2645.68.

Do you want further details or have additional questions?

Here are 5 related questions to expand on this problem:

1. What is the general form of an exponential growth equation?
2. How does exponential growth differ from linear growth, as seen in Figure 3?
3. How can the growth rate in $y = 583(1.05)^x$ be interpreted in percentage terms?
4. What happens to the curve if the growth rate is less than 1?
5. How would you determine the doubling time for this exponential function?

Tip: Exponential growth models are widely used in finance, biology, and physics to describe rapid increases over time. Understanding these models is critical for interpreting real-world trends!