Bytelearn - cat image with glassesAI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Which type of function best models this data?






x

Y


-2
2.4


-1
0.2


0
0


1
1


2
5


3
10


4
17

22) Which type of function best models this data?\newline\begin{tabular}{|c|c|}\newline\hlinex x & Y Y \\\newline\hline2-2 & 22.44 \\\newline\hline1-1 & 00.22 \\\newline\hline 00 & 00 \\\newline\hline 11 & 11 \\\newline\hline 22 & 55 \\\newline\hline 33 & 1010 \\\newline\hline 44 & 1717 \\\newline\hline\newline\end{tabular}

Full solution

Q. 22) Which type of function best models this data?\newline\begin{tabular}{|c|c|}\newline\hlinex x & Y Y \\\newline\hline2-2 & 22.44 \\\newline\hline1-1 & 00.22 \\\newline\hline 00 & 00 \\\newline\hline 11 & 11 \\\newline\hline 22 & 55 \\\newline\hline 33 & 1010 \\\newline\hline 44 & 1717 \\\newline\hline\newline\end{tabular}
  1. Analyze Data Points: Step 11: Analyze the data points to see if they fit a linear, quadratic, or other type of function.\newlineData Points: (2,2.4),(1,0.2),(0,0),(1,1),(2,5),(3,10),(4,17)(-2, 2.4), (-1, 0.2), (0, 0), (1, 1), (2, 5), (3, 10), (4, 17)\newlineCheck for a linear pattern by calculating the differences between consecutive yy-values.\newlineDifferences: 0.22.4=2.20.2 - 2.4 = -2.2, 00.2=0.20 - 0.2 = -0.2, 10=11 - 0 = 1, 51=45 - 1 = 4, 105=510 - 5 = 5, 1710=717 - 10 = 7\newlineSince differences are not constant, it's not linear.
  2. Check for Quadratic Pattern: Step 22: Check for a quadratic pattern by calculating the differences of the differences (second differences).\newlineSecond Differences: 2.2(0.2)=2-2.2 - (-0.2) = -2, 1(0.2)=1.21 - (-0.2) = 1.2, 41=34 - 1 = 3, 54=15 - 4 = 1, 75=27 - 5 = 2\newlineSince second differences are not constant, it's not a perfect quadratic but it seems to be closer to quadratic than linear.
  3. Plot Points for Best Fit: Step 33: Plot the points to visually determine the best fit.\newlinePlotting points on a graph, the shape of the curve appears to be more parabolic, suggesting a quadratic function might be a better fit despite the imperfect second differences.

More problems from Find terms of a geometric sequence