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

Explanation:

Step1: Test x=0 in each option

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

Step2: Test x=1 in B and C

• Option B: \( y = 33(1)+32.7 = 65.7 \), table has y=67. Close.
• Option C: \( y = 33\sqrt{1}+32.7 = 33 + 32.7 = 65.7 \), same as B here.

Step3: Test x=2 in B and C

• Option B: \( y = 33(2)+32.7 = 66 + 32.7 = 98.7 \), table has y=79. Not close.
• Option C: \( y = 33\sqrt{2}+32.7 \approx 33(1.414)+32.7 \approx 46.66 + 32.7 \approx 79.36 \), very close to 79.

Step4: Confirm with x=3

• Option C: \( y = 33\sqrt{3}+32.7 \approx 33(1.732)+32.7 \approx 57.16 + 32.7 \approx 89.86 \), close to 91.
• Option B: \( y = 33(3)+32.7 = 99 + 32.7 = 131.7 \), way off.

Answer:

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