the data points show the area y (in square kilometers) that a certain forest covers after being inhabited…

the data points show the area y (in square kilometers) that a certain forest covers after being inhabited for a time x (in years).\neach figure has the same data points.\nhowever, each figure has a different curve fitting the data.\nthe equation for each curve is also shown.\nanswer the questions that follow.\nfigure 1\nfigure 2\nfigure 3\n(a) which curve fits the data best?\nfigure 1 figure 2 figure 3\n(b) use the equation of the best fitting curve from part (a) to predict the area\nthat the forest covers after it is inhabited for 15 years. round your answer to\nthe nearest hundredth.\nsquare kilometers

the data points show the area y (in square kilometers) that a certain forest covers after being inhabited for a time x (in years).\neach figure has the same data points.\nhowever, each figure has a different curve fitting the data.\nthe equation for each curve is also shown.\nanswer the questions that follow.\nfigure 1\nfigure 2\nfigure 3\n(a) which curve fits the data best?\nfigure 1 figure 2 figure 3\n(b) use the equation of the best fitting curve from part (a) to predict the area\nthat the forest covers after it is inhabited for 15 years. round your answer to\nthe nearest hundredth.\nsquare kilometers

Answer

Explanation:

Step1: Analyze the data points and curves

  • Figure 1 has a linear equation (y = - 75x+1600). The data points do not seem to follow a linear trend closely as the rate of decrease is not constant.
  • Figure 2 has an exponential equation (y = 2483(0.92)^{x}). The data points are closer to this curve compared to Figure 1.
  • Figure 3 has an exponential equation (y=2500(0.81)^{x}). The data points are not as close to this curve as they are to the curve in Figure 2.

Step2: Predict the area for (x = 15) using the equation of Figure 2

Substitute (x = 15) into (y = 2483(0.92)^{x}) [ \begin{align*} y&=2483\times(0.92)^{15}\ &=2483\times0.286356\ &=701.02 \end{align*} ]

Answer:

(a) Figure 2 (b) (701.02) square kilometers