Question

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 = 148.4sqrt{x - 1}-154)
b. (y=-46.4x + 191.7)
c. (y = 148.4sqrt{x - 1}+154)
d. (y = 46.4x + 191.7)

Explanation:

Step1: Analyze the trend of data

The number of units sold is increasing over time, so we can rule out option B which has a negative - slope ($y=-46.4x + 191.7$).

Step2: Test option A

When $x = 1$, for $y = 148.4\sqrt{x - 1}-154$, $\sqrt{1 - 1}=0$, then $y=-154$. But when $x = 1$, the actual $y = 150$, so option A is incorrect.

Step3: Test option C

When $x = 1$, for $y = 148.4\sqrt{x - 1}+154$, $\sqrt{1 - 1}=0$, then $y = 154$. When $x = 2$, $y=148.4\sqrt{2 - 1}+154=148.4 + 154=302.4\approx300$.

Step4: Test option D

When $x = 1$, $y=46.4\times1+191.7=238.1
eq150$.

Answer:

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