Question

The cost in dollars of producing x vehicles for a company is given by C(x)=1200x+5500


Interpret the rate of change of this linear function.

Answer 1

The rate of change represents the variable production cost rate. The production cost is increased in 1200 units per each additional manufactured car.

Interpretation of a linear function

Let be $C$ and $x$ the production cost and the number of vehicles produced, it there is a linear relationship between the two variables, then we have the following formula:

$C(x) = \dot r \cdot x + C_{o}$ (1)

Where:

• $C_{o}$ - Fixed production costs.
• $\dot r$ - Variable production cost rate.

In a nutshell, the rate of change represents the variable production cost rate. The production cost is increased in 1200 units per each additional manufactured car. $\blacksquare$

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