Chapter 3.1, Problem 12AYU

A car has 12,500 miles on its odometer. Say the car is driven an average of 40 miles per day. Choose the model that expresses the number of miles $N$ that will be on its odometer after $x$ days.

a. $N\left(x\right)=-40x+12,500$

b. $N\left(x\right)=40x-12,500$

c. $N\left(x\right)=12,500x+40$

d. $N\left(x\right)=40x+12,500$

To determine

To calculate: The model of the linear equation that expresses the number of miles $\text{N}$ that will be on the odometer after $x$ days.

Answer to Problem 12AYU

Solution:

d. $N(x) = 40x + 12500$

Explanation of Solution

Given:

A car has 12500 miles on its odometer. The average speed of the car is 40 miles per day.

a. $N(x) = -40x + 12,500$

b. $N(x) = 40x - 12,500$

c. $N(x) = 12,500x + 40$

d. $N(x) = 40x + 12,500$

Formula Used:

The average rate of change of the function is the slope of that function.

The $y\text{-intercept}$ $b$, of the function is the value of the function at 0.

Using the above information, we get the function as $f(x) = mx + b$.

Calculation:

Let the model of the car be $N(x) = mx + b$.

The average rate of change of miles per day is 40 miles.

Therefore, we get $m = 40$.

12500 miles is already on the odometer.

Therefore, the value of the function at 0 is 12500.

Thus, the model that expresses the number of miles that will be on the odometer after $x$ days is

$N(x) = 40x + 12500$