Question

A tire manufacturing plant produces 500 tires a day on average. If the production of tires isrepresented by a function where f represents the number of tires produced over x days,which equation best models the function f(x)?A f(x) = 500 + xB f(x) = 500 - XC f(x) = 500xD f(x) = 500%

Answer 1

In linear equations, the slope (or rate of change) is represented by m in the next equation:

y = mx + b [1]

We have to remember that b is the intercept at y when x = 0.

Considering that the tire manufacturing plant produces 500 tires a day, and this "tells" us that is this is a rate of change, we can say that the function should be (that is, the function that represents the number of tires produced over x days):

f(x) = 500x

This function "tells" us also that when the production started, x = 0, there were no tires (b = 0).

To check this, we can imagine that every day we produce 500 tires; the next day, another 500 tires, and so on.

Thus, over 2 days, we have that the number of tires produced over 2 days is:

f(2) = 500*(2) = 1000 tires

Over three days:

f(3) = 500*(3) = 1500 tires.

And so forth.

Then, the equation that best models the function that represents the number of tires produced over x days is option C, f(x) = 500x.