Question

figure 1
figure 2
figure 3
(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 area that the forest covers after it is inhabited for 13 years. round your answer to the nearest hundredth.
square kilometers

Explanation:

Step1: Observe the data - point distribution

By visually inspecting the scatter - plots, the data points in Figure 3 seem to follow a parabolic pattern more closely compared to the linear pattern in Figure 1 and the exponential pattern in Figure 2. So, Figure 3 provides the best fit.

Step2: Substitute \(x = 13\) into the quadratic equation

The equation of the best - fitting curve from Figure 3 is \(y=9.1x^{2}-275x + 2450\). Substitute \(x = 13\) into this equation:
\[

$$\begin{align*} y&=9.1\times(13)^{2}-275\times13 + 2450\\ &=9.1\times169-3575+2450\\ &=1537.9-3575 + 2450\\ &=1537.9+2450-3575\\ &=4987.9 - 3575\\ &=1412.9 \end{align*}$$

\]

Answer:

(a) Figure 3
(b) 1412.90 square kilometers