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Determine the square root function that best models the given data.

Miles recorded his height, in inches, from age 10 to age 18, as shown in the table:

[tex]\[
\begin{tabular}{|l|c|c|c|c|c|c|c|c|c|}
\hline Age, $x$ & 10 & 11 & 12 & 13 & 14 & 15 & 16 & 17 & 18 \\
\hline Height, $y$ & 54 & 58 & 61.5 & 64.5 & 68 & 70 & 73 & 74 & 74.5 \\
\hline
\end{tabular}
\][/tex]

What is the square root function that best models this set of data?

[tex]\[ y = \sqrt{x} + \][/tex]

Choices:
- 9.12
- 29.41
- 2.64
- 43.64
- 10.76


Sagot :

To model the given data set with a square root function of the form [tex]\(y = a \sqrt{x - b} + c\)[/tex], we can use the provided coefficients [tex]\(a, b, c\)[/tex]. Here is the detailed explanation:

The problem asks for the model in the form:
[tex]\[ y = a \sqrt{x - b} + c \][/tex]

From the given data and calculated coefficients, we know:
1. [tex]\(a = 10.76\)[/tex]
2. [tex]\(b = 9.12\)[/tex]
3. [tex]\(c = 43.64\)[/tex]

Thus, substituting these values into the equation, we get:
[tex]\[ y = 10.76 \sqrt{x - 9.12} + 43.64 \][/tex]

So the fully formed square root function that best models the set of data is:
[tex]\[ y = 10.76 \sqrt{x - 9.12} + 43.64 \][/tex]

To match this equation with the provided mathematical expression template:

[tex]\[ y = \underbrace{10.76}_{a} \sqrt{ x - \underbrace{9.12}_{b} } + \underbrace{43.64}_{c} \][/tex]

Therefore, when you drag the numbers into the correct locations, it should look like this:
[tex]\[ y = \text{10.76} \sqrt{x - \text{9.12}} + \text{43.64} \][/tex]
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