answer the questions that follow.\nfigure 1\nfigure 2\nfigure 3\n(a) which curve fits the data best?\nfigure…

Explanation:

Step1: Analyze the data - point distribution

By observing the scatter - plots, in Figure 1, the curve $y = 200(0.93)^{x}+50$ seems to follow the general trend of the data points well. In Figure 2, the curve $y = 504(0.98)^{x}$ has a steeper decay than the data points suggest. In Figure 3, the linear function $y=-0.26x + 380$ does not capture the non - linear decay pattern of the data. So, Figure 1 has the best - fitting curve.

Step2: Substitute $x = 80$ into the best - fitting equation

The best - fitting equation is $y = 200(0.93)^{x}+50$. Substitute $x = 80$ into it: $y=200\times(0.93)^{80}+50$. First, calculate $(0.93)^{80}$. Let $a=(0.93)^{80}$. Using the formula $a = e^{80\ln(0.93)}$. $\ln(0.93)\approx- 0.0725$, then $80\ln(0.93)\approx80\times(-0.0725)=-5.8$. $e^{-5.8}\approx0.00304$. $200\times(0.93)^{80}=200\times0.00304 = 0.608$. $y=0.608 + 50=50.608\approx50.61$.

Answer:

(a) Figure 1 (b) $50.61$