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

Explanation:

Step1: Test x=0

For option A: \( y = 33(0)+32.7 = 32.7 \), but table has y=32. Close.
For option B: \( y = 33\sqrt{0}+32.7 = 32.7 \), close to 32.
For option C: \( y = 33\sqrt{0}-32.7 = -32.7 \), wrong.
For option D: \( y = 33(0)-32.7 = -32.7 \), wrong.

Step2: Test x=1

For option A: \( y = 33(1)+32.7 = 65.7 \), table has y=67. Close.
For option B: \( y = 33\sqrt{1}+32.7 = 33 + 32.7 = 65.7 \), close to 67.

Step3: Test x=4 (sqrt(4)=2)

For option B: \( y = 33(2)+32.7 = 66 + 32.7 = 98.7 \), table has y=98. Very close.
For option A: \( y = 33(4)+32.7 = 132 + 32.7 = 164.7 \), table has y=98. Wrong.

Answer:

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