Question

however, each figure has a different curve fitting the data. the equation for each curve is also shown. answer the questions that follow. figure 1 figure 2 figure 3 (a) which curve fits the data best?

Explanation:

Step1: Visual inspection

Visually assess how closely the curves follow the data - points. In Figure 1, the exponential decay curve $y = 531(0.98)^x$ seems to pass through or near most of the data - points. In Figure 2, the curve $y=200(0.93)^x + 50$ does not fit well as there are significant vertical distances between the data - points and the curve. In Figure 3, the quadratic curve $y = 0.03x^{2}-8x + 575$ also has some data - points that are far from the curve.

Step2: Consider goodness - of - fit measures

Although not calculated here (since no specific measures like R - squared are given), visually Figure 1 has the best approximation of the data - points.

Answer:

The curve $y = 531(0.98)^x$ (Figure 1) fits the data best.