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\hline X \mathrm{X} & Y \mathrm{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\hline X \mathrm{X} & Y \mathrm{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 determine the pattern or trend.\newlineGiven data points:\newline(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)\newlinePlotting these points or calculating differences can help identify if the relationship is linear, quadratic, or another type.
  2. Calculate First Differences: Step 22: Calculate first differences between consecutive yy-values to check for linearity.\newlineFirst differences: 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\newlineThese differences are not constant, suggesting the data is not linear.
  3. Calculate Second Differences: Step 33: Calculate second differences to check for a quadratic relationship.\newlineSecond differences: 0.2(2.2)=2-0.2 - (-2.2) = 2, 1(0.2)=1.21 - (-0.2) = 1.2, 41=34 - 1 = 3, 54=15 - 4 = 1, 75=27 - 5 = 2\newlineThese differences are not constant, indicating the data might not be quadratic.
  4. Consider Alternative Functions: Step 44: Consider higher-degree polynomials or other functions.\newlineGiven the increasing rate of change, a higher-degree polynomial might be suitable. Alternatively, exponential or other non-linear models could be considered.

More problems from Find terms of a geometric sequence