Question

A car manufacturer is reducing the number of incidents with the transmission by issuing a voluntary recall. During week 3 of the recall, the manufacturer fixed 391 cars. In week 13, the manufacturer fixed 361 cars. Assume that the reduction in the number of cars each week is linear. Write an equation in function form to show the number of cars seen each week by the mechanic.

f(x) = 3x + 400
f(x) = 3x + 391
f(x) = −3x + 391
f(x) = −3x + 400

please explain ;-;

Answer 1

f(x) = -3x + 400.

Explanation:

To write the equation in function form to represent the number of cars seen each week by the mechanic, we need to consider the given information.

Let's define:

x: the number of weeks since the start of the recall.

Given that the reduction in the number of cars each week is linear, we can determine the equation by considering the initial number of cars fixed and the reduction rate.

In week 3, the manufacturer fixed 391 cars, which indicates that in the third week (x = 3), the number of cars fixed is 391. This gives us a reference point.

Now, we can find the equation in the form f(x) = mx + b, where m represents the slope (reduction rate) and b represents the initial value (number of cars fixed in the starting week).

To find the slope (m):

We need to determine the change in the number of cars fixed from week 3 (x = 3) to week 13 (x = 13).

The change in x is 13 - 3 = 10.

The change in the number of cars fixed is 361 - 391 = -30.

The slope (m) represents the rate of change, so we calculate it as:

m = (change in the number of cars fixed) / (change in x) = -30 / 10 = -3

Now, we have the slope (m = -3).

To find the initial value (b), we substitute the values of x and f(x) into the equation:

f(3) = 391

Plugging in the values:

-3(3) + b = 391

Simplifying the equation:

-9 + b = 391

Solving for b:

b = 391 + 9 = 400

Now, we have the slope (m = -3) and the initial value (b = 400).

Therefore, the equation representing the number of cars seen each week by the mechanic is:

f(x) = -3x + 400