(a) which curve fits the data best? figure 1 figure 2 figure 3 (b) use the equation of the best - fitting…

Explanation:

Step1: Visual inspection

Visually, Figure 1 and Figure 2 have exponential - decay functions ($y = 531(0.98)^x$ and $y=200(0.93)^x + 50$), which are typically for decay processes. Figure 3 has a quadratic function ($y = 0.03x^2-8x + 575$). Since the data points seem to follow a decay - like pattern more closely and the points in Figure 1 seem to be closer to the curve compared to Figure 2, Figure 1 fits the data best.

Step2: Prediction using the best - fitting equation

The best - fitting equation is $y = 531(0.98)^x$. Substitute $x = 30$ into the equation. $y=531\times(0.98)^{30}$ First, calculate $(0.98)^{30}$. Using the formula $a^n=e^{n\ln(a)}$, we have $\ln(0.98)\approx - 0.0202$ and $n = 30$, so $n\ln(a)=30\times(-0.0202)=-0.606$. Then $(0.98)^{30}=e^{- 0.606}\approx0.545$. Now, $y = 531\times0.545=289.395\approx289.40$

Answer:

(a) Figure 1 (b) $289.40$