Jamal owns a parking garage and is trying to find the relationship between hour of the day and number of cars in the garage. He finds that between 4 am and 10 am he can model this with a linear relationship. The equation for this model is

y = 3.96x + 2. About how many cars are entering the garage every hour?

A 1
B 2
C 3
D 4

1 answer

In the equation \( y = 3.96x + 2 \), \( y \) represents the number of cars in the garage, and \( x \) represents the hour of the day (with \( x = 0 \) corresponding to 4 a.m.).

The coefficient of \( x \) in the equation is \( 3.96 \), which indicates the rate of change of the number of cars with respect to time. In this case, it suggests that for each additional hour (\( x \) increases by 1), the number of cars in the garage increases by approximately \( 3.96 \) cars.

To find out how many cars are entering the garage every hour, we interpret the coefficient \( 3.96 \) as the number of cars entering each hour. Since the option choices are whole numbers, we can round \( 3.96 \) to \( 4 \).

Thus, about 4 cars are entering the garage every hour.

The answer is \( \text{D} , 4 \).