Question

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.
A. none of these
B. quadratic
C. linear
D. exponential

Answer 1

The option c is correct. The linear representation model is best for this situation out of the exponential, quadratic model.

According to the statement

we have given that:

Monthly Rate = $20, Number of customers = 5000

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

And we have to find that The type of model that best fits the given situation.

So, according to the linear representation model

Monthly Rate = $20, Number of customers = 5000

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

Here, we can see that there is a linear change in the number of customers whenever there is decrease in the monthly rate.

We have 2 pair of values here,

x = 20, y = 5000

x = 19, y = 5500

Let us write the equation in slope intercept form:

y = mx + c

And Slope of a function is

m = y₂ - y₁ / x₂ - x₁

Then

m = 5500 - 5000 / 19 - 20

m = -500

So, the equation become

y = -500x +c

And find the value of by putting the values.

So, c = 15000

And the equation become

y = -500x + 15000.

According to this linear model is perfect for this situation.

So, The linear representation model is best for this situation.

Learn more about linear representation here

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