Question

select the correct answer. which equation best models the set of data in this table?

x	0	1	2	3	4	5	6	7	8	9
y	32	67	79	91	98	106	114	120	126	132

a. $y = 33sqrt{x}+32.7$
b. $y = 33x + 32.7$
c. $y = 33sqrt{x}-32.7$
d. $y = 33x - 32.7$

Explanation:

Step1: Substitute \(x = 0\) into each equation

When \(x = 0\), for option A: \(y=33\sqrt{0}+32.7=32.7\); for option B: \(y = 33\times0+32.7 = 32.7\); for option C: \(y=33\sqrt{0}-32.7=- 32.7\); for option D: \(y=33\times0 - 32.7=-32.7\). In the table, when \(x = 0\), \(y = 32\), option A and B are closer to 32 compared to C and D.

Step2: Substitute \(x = 1\) into options A and B

For option A: \(y=33\sqrt{1}+32.7=33 + 32.7=65.7\). For option B: \(y=33\times1+32.7=33 + 32.7 = 65.7\).

Step3: Substitute \(x = 2\) into options A and B

For option A: \(y=33\sqrt{2}+32.7\approx33\times1.414+32.7=46.662+32.7 = 79.362\). For option B: \(y=33\times2+32.7=66 + 32.7=98.7\). In the table, when \(x = 2\), \(y = 79\), option A is closer.

Answer:

A. \(y = 33\sqrt{x}+32.7\)