The equations to be used in the question are provided with which the data
in the table can be compared.
- The equation that models the set of data is; [tex]\underline{y = 33 \cdot \sqrt{x} + 32.7}[/tex]
Reasons:
The data is presented in the following table.
[tex]\begin{tabular}{c|c|c|c|c|c|c|c|c|c|c|}x&0&1&2&3&4&5&6&7&8&9\\y&32&67&79&91&98&106&114&120&126&132\end{array}\right][/tex]
The given options are;
A. [tex]y = 33 \cdot \sqrt{x - 32.7}[/tex]
B. y = 33·√x + 32.7
C. y = 33·x + 32.7
D. y = 33·x - 32.7
At x = 0, we have;
Option A; y = An imaginary number
Option B; y = 33 × √0 + 32.7 = 32.7
Option C; y = 33 × 0 + 32.7 = 32.7
Option D; y = 33 × 0 - 32.7 = -32.7
Therefore, the likely options are option B and option C
However, at x = 9, we get;
Option B; y = 33 × √9 + 32.7 = 131.7
Option C; y = 33 × 9 + 32.7 = 329.7
Therefore, the most likely correct option is option B
The output values for option B are;
[tex]\begin{tabular}{c|c|c|c|c|c|c|c|c|c|c|}x&0&1&2&3&4&5&6&7&8&9\\y&32&67&79&91&98&106&114&120&126&132\\Option B; y&32.7&65.7&79.4&89.9&98.7&106.49&113.53&120.0&126.04&131.7\end{array}\right][/tex]
Therefore, the equation that best models the set of data is option B;
Option B; y = 33·√x + 32.7
Learn more about model equations here:
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