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

The linear model for the cost of producing x humidifiers is of the form C = mx + b, where m is the slope (the rate of change of cost with respect to the number of humidifiers produced) and b is the y-intercept (the fixed cost, or the cost when no humidifiers are produced). Looking at the data, when x = 0 (i.e. no humidifiers produced) the cost is 87, so b = 87. Also, when x = 100, the cost is approximately 192, so we can use these two points to find the slope: 192 = 100m + 87, so m = 1.05. Therefore, the linear model is C = 87 + 1.05x, which is choice (C).

The Following Table Shows Data for the Cost of Humidifiers