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Determine what type of model best fits the given situation: an internet phone company presently provides service to 5,000 customers at a monthly rate of $20 per month. after a market survey, it was determined that for each $1 decrease in the monthly rate an increase of 500 new customers would result.

Sagot :

The expression [tex]$-500 \times 18+15000=-9000+15000=6000[/tex] which best fit exists in the Linear model.

How to estimate the linear model?

Given: Monthly Rate = $20

Number of customers = 5000

If there exists a decrease of $1 in the monthly rate, the number of customers increases by 500.

Let us decrease the monthly rate by $1.

Monthly Rate = $20 - $1 = $19

Number of customers = 5000 + 500 = 5500

Let us decrease the monthly rate by $1 more.

Monthly Rate = $19 - $1 = $18

Number of customers = 5500 + 500 = 6000

Linear change in the number of customers whenever there exists a decrease in the monthly rate.

We have 2 pairs of values here,

x = 20, y = 5000

x = 19, y = 5500

The equation in slope-intercept form: y = mx + c

The slope of a function: [tex]${data-answer}amp;m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}} \\[/tex]

[tex]${data-answer}amp;m=\frac{5500-5000}{19-20} \\[/tex]

[tex]${data-answer}amp;\Rightarrow-500[/tex]

So, the equation is y = -500x + c

Putting x = 20, y = 5000:

[tex]${data-answer}amp;5000=-500 \times 20+c \\[/tex]

[tex]${data-answer}amp;\Rightarrow c=5000+10000=15000 \\[/tex]

[tex]${data-answer}amp;\Rightarrow \mathbf{y}=-500 \mathbf{x}+15000[/tex]

Whether (18,6000) satisfies it.

Putting x = 18

[tex]$-500 \times 18+15000=-9000+15000=6000[/tex]

Therefore, the expression [tex]$-500 \times 18+15000=-9000+15000=6000[/tex] which best fits exist Linear model.

To learn more about the linear model refer to:

https://brainly.com/question/6110794

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