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
units, y	150	300	380	425	425	480	520	550	575

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

Explanation:

Step1: Check the trend of data

As $x$ (month) increases, $y$ (units) also increases. So the slope of the linear - like model should be positive. Option A has a negative slope ($-46.4$), so we can eliminate option A.

Step2: Test a data - point

Let's take the first data - point $(x = 1,y = 150)$.
For option B: When $x = 1$, $y=46.4\times1 + 191.7=46.4 + 191.7 = 238.1
eq150$.
For option C: When $x = 1$, $y = 148.4\sqrt{1 - 1}+154=154$, which is close to $150$.
For option D: When $x = 1$, $y = 148.4\sqrt{1 - 1}-154=-154
eq150$.

Step3: Test another data - point

Let's take $x = 2$.
For option C: $y = 148.4\sqrt{2 - 1}+154=148.4 + 154 = 302.4$, which is close to $300$.

Answer:

C. $y = 148.4\sqrt{x - 1}+154$