2) Which type of function best models this data?\begin{tabular}{|c|c|}\hline X & Y \\\hline−2 & 2.4 \\\hline−1 & 0.2 \\\hline 0 & 0 \\\hline 1 & 1 \\\hline 2 & 5 \\\hline 3 & 10 \\\hline 4 & 17 \\\hline\end{tabular}
Q. 2) Which type of function best models this data?\begin{tabular}{|c|c|}\hline X & Y \\\hline−2 & 2.4 \\\hline−1 & 0.2 \\\hline 0 & 0 \\\hline 1 & 1 \\\hline 2 & 5 \\\hline 3 & 10 \\\hline 4 & 17 \\\hline\end{tabular}
Analyze Data Points: Step 1: Analyze the data points to determine the pattern or trend.Given data points:(−2,2.4),(−1,0.2),(0,0),(1,1),(2,5),(3,10),(4,17)Plotting these points or calculating differences can help identify if the relationship is linear, quadratic, or another type.
Calculate First Differences: Step 2: Calculate first differences between consecutive y-values to check for linearity.First differences: 0.2−2.4=−2.2, 0−0.2=−0.2, 1−0=1, 5−1=4, 10−5=5, 17−10=7These differences are not constant, suggesting the data is not linear.
Calculate Second Differences: Step 3: Calculate second differences to check for a quadratic relationship.Second differences: −0.2−(−2.2)=2, 1−(−0.2)=1.2, 4−1=3, 5−4=1, 7−5=2These differences are not constant, indicating the data might not be quadratic.
Consider Alternative Functions: Step 4: Consider higher-degree polynomials or other functions.Given the increasing rate of change, a higher-degree polynomial might be suitable. Alternatively, exponential or other non-linear models could be considered.
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