figure 1\nfigure 2\nfigure 3\n(a) which curve fits the data best?\nfigure 1 figure 2 figure 3\n(b) use the…

figure 1\nfigure 2\nfigure 3\n(a) which curve fits the data best?\nfigure 1 figure 2 figure 3\n(b) use the equation of the best fitting curve from part (a) to predict the value of the item at a time 12 years after its purchase. round your answer to the nearest hundredth.\n$$

figure 1\nfigure 2\nfigure 3\n(a) which curve fits the data best?\nfigure 1 figure 2 figure 3\n(b) use the equation of the best fitting curve from part (a) to predict the value of the item at a time 12 years after its purchase. round your answer to the nearest hundredth.\n$$

Answer

Explanation:

Step1: Observe data - point proximity

Visually, in Figure 1, the data - points are closest to the curve. In Figure 2, the data - points deviate more from the curve, and in Figure 3, the linear model does not capture the curvature of the data well. So, Figure 1 has the best - fitting curve.

Step2: Identify the best - fitting curve's equation

The equation of the best - fitting curve (from Figure 1) is $y = 54(1.13)^{x}$.

Step3: Substitute $x = 12$

We want to find the value when $x = 12$. Substitute $x = 12$ into the equation $y = 54(1.13)^{x}$. So, $y=54\times(1.13)^{12}$.

Step4: Calculate the value

First, calculate $(1.13)^{12}\approx4.36349$. Then, $y = 54\times4.36349\approx235.63$.

Answer:

(a) Figure 1 (b) $235.63$