Question

(a) which curve fits the data best?
○ figure 1 ○ figure 2 ○ figure 3
(b) use the equation of the best - fitting curve from part (a) to predict the amount of money in the account after 37 years. round your answer to the nearest hundredth.
$

Explanation:

Step1: Analyze the data - points distribution

Visually, if the data - points seem to follow a linear pattern, a linear function is a good fit; if they show exponential growth or decay, an exponential function is appropriate; and if they have a parabolic shape, a quadratic function is suitable. From the given graphs, if the data - points seem to grow at an increasing rate over time, the exponential function is likely the best fit. Here, Figure 2 with the exponential function $y = 609(1.05)^x$ seems to follow the data - points' trend better as it shows a non - linear growth which is often seen in compound - growth type of data.

Step2: Substitute $x = 37$ into the exponential function

We have the function $y=609(1.05)^x$. Substitute $x = 37$ into it:
\[y=609\times(1.05)^{37}\]
First, calculate $(1.05)^{37}$. Using a calculator, $(1.05)^{37}\approx6.0881$. Then, $y = 609\times6.0881$.
\[y=609\times6.0881 = 3707.6529\]
Rounding to the nearest hundredth, $y\approx3707.65$.

Answer:

(a) Figure 2
(b) $3707.65$