Question

the pool fun company has learned that by pricing a newly released fun noodle at $2 sales will reach 9000 fun noodles per day in the summer. raising the price to $4 will cause the sales to fall to 3000 fun noodles per day. assume the relationship Between sales price x and number fun noodles sold, y is linear.a. the equation is (slope intercept form) b. predict the daily sales of fun noodles if the price is $3.50

Answer 1

Sales price (x) is the independent variable

Number of Fun Noodles Sold (y) is the dependent variable

Given the two information, we can write 2 coordinate points as shown:

`\begin{gathered} (x_1,y_1)=(2,9000) \\ \text{and} \\ (x_2,y_2)=(4,3000) \end{gathered}`a)

We can use the point slope formula for a line to determine the slope intercept form [y = mx + b]. Shown below:

`\begin{gathered} y-y_1=m(x-x_1) \\ y-y_1=(y_2-y_1)/(x_2-x_1)(x-x_(1)) \\ \\ y-9000=(3000-9000)/(4-2)(x-2) \\ y-9000=-(6000)/(2)(x-2) \\ y-9000=-3000(x-2) \\ y=-3000(x-2)+9000 \\ y=-3000x+6000+9000 \\ y=-3000x+15,000 \end{gathered}`

This is the slope intercept form of the line:

`y=-3000x+15,000`b)

We want to find the sales, y, for sale price, x, of 3.50.

We simply plug 3.5 into x and find the value of y:

`\begin{gathered} y=-3000x+15,000 \\ y=-3000(3.5)+15,000 \\ y=4500 \end{gathered}`

Daily Sales at $3.50 would be around $4500