Question

If the cost is a function depending in the number of sections, how much will 200 sections cost?

A. 7,400
B. 7,439
C. 7,556
D. 7,837

Answer 1

It will cost $7439.

We first find the rate of change between consecutive points. Between the first two,

m = (1889-409)/(50-10) = 1480/40 = 37

Between the second two points,

m = (4664-1889)/(125-50) = 2775/75 = 37

Since the rate of change is the same between points, this is a linear situation.

Writing the equation of the line in point-slope form, we have

y - 409 = 37(x - 10)

Using 200 as x,

y - 409 = 37(200 - 10)

y - 409 = 37(190)

y - 409 = 7030

Adding 409 to both sides,

y = 7030 + 409 = 7439

Answer 2

Assuming that the relationship is linear, to get the cost of 200 sections we shall proceed as follows:
slope,m=(4664-1889)/(125-50)=37
thus the model will be:
m(x_1-x)=(y_1-y)
thus
37(x-10)=y-409
37x-370=y-409
y=37x+39
thus the cost of 200 sections will be:
y=37(200)+39
y=7439

Answer: B] 7439