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

Answer 1

Answer:

The best fit is A. Linear model

Step-by-step explanation:

Given:

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.

To find:

The type of model that best fits the given situation?

Solution:

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:

$y =mx+c$

Slope of a function:

$m=\dfrac{y_2-y_1}{x_2-x_1}$

$m=\dfrac{5500-5000}{19-20}\\\Rightarrow -500$

So, the equation is:

$y =-500x+c$

Putting x = 20, y = 5000:

$5000 =-500\times 20+c\\\Rightarrow c = 5000 +10000 = 15000$

$\Rightarrow \bold{y =-500x+15000}$

Let us check whether (18, 6000) satisfies it.

Putting x = 18:

$-500 \times 18 +15000 = -9000+15000 = 6000$ so, it is true.

So, the answer is:

The best fit is A. Linear model