Question

select the correct answer
a company manufactures acoustic guitars. the table shows the number of units that the company sold each month over a nine - month period beginning in january

month, x	1	2	3	4	5	6	7	8	9

which equation best models the situation?
a. $y = 46.4x + 191.7$
b. $y = - 46.4x + 191.7$
c. $y = 148.4\sqrt{x - 1}-154$
d. $y = 148.4\sqrt{x - 1}+154$

Explanation:

Step1: Analyze Trend

The number of units sold (y) increases as the month (x) increases, so the slope should be positive. Eliminate option B (negative slope) and option C (subtraction at the end, which would lower values).

Step2: Test Option A

For \( x = 1 \), \( y = 46.4(1) + 191.7 = 238.1 \), but the actual \( y \) is 150. Not matching.

Step3: Test Option D

For \( x = 1 \), \( y = 148.4\sqrt{1 - 1} + 154 = 154 \), close to 150. For \( x = 2 \), \( y = 148.4\sqrt{2 - 1} + 154 = 148.4 + 154 = 302.4 \), close to 300. For \( x = 9 \), \( y = 148.4\sqrt{9 - 1} + 154 = 148.4\times2.828 + 154 \approx 419.7 + 154 = 573.7 \), close to 575. This fits better.

Answer:

D. \( y = 148.4\sqrt{x - 1} + 154 \)