The following table shows data for the cost of humidifiers based on the number of humidifiers produced. Find a linear model for the cost C of producing x humidifiers.
A) C = 1.05 + 87 x
B) C = 1.05 x
C) C = 87 + 1.05 x
D) C = 87 + 20 x
E) C = 87 x

Question

The following table shows data for the cost of humidifiers based on the number of humidifiers produced. Find a linear model for the cost C of producing x humidifiers. 
A) C = 1.05 + 87 x 
B) C = 1.05 x 
C) C = 87 + 1.05 x 
D) C = 87 + 20 x 
E) C = 87 x

Quizplus · Accepted Answer

We are looking for a linear model, which takes the form of C = mx + b, where m is the slope and b is the y-intercept. In this case, we are given data points (x, C) and need to find the slope and y-intercept that best fit these data points. The best choice is C = 87 + 1.05x because the slope of 1.05 represents the rate of increase in cost per unit of humidifier produced and the y-intercept of 87 represents the base cost of producing zero humidifiers. This linear model fits the data points well and accurately represents the relationship between the number of humidifiers produced and the total cost of production.

The Following Table Shows Data for the Cost of Humidifiers