Question

the data points show the area y (in square kilometers) that a certain forest covers after being inhabited for a time x (in years). each figure has the same data points. 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 y = 1250(0.91)^x y=-75x + 1600 y = 2476(0.92)^x (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

Explanation:

Step1: Observe data - point proximity

Visually check which curve is closest to most data - points. In Figure 3, the curve passes closer to more data - points compared to Figure 1 and Figure 2.

Step2: Predict area using best - fit equation

The best - fitting curve is \(y = 2476(0.92)^{x}\). Substitute \(x = 13\) into the equation.
\[y=2476\times(0.92)^{13}\]
\[y = 2476\times0.337977\]
\[y\approx837.83\]

Answer:

(a) Figure 3
(b) 837.83 square kilometers