Question

the table shows the cost, y, when a bike is rented for x number of hours. bike rentals hour x cost y 0 4 1 5.5 3 8.5 5 11.5 7 14.5 what is the meaning of the initial value and the rate of change for the situation? a the initial base charge to rent a bike is $1.50 and the additional hourly charge for the bike rental is $4.00 per hour. b the initial base charge to rent a bike is $4.00 and the additional hourly charge for the bike rental is $3.00 per hour. c the initial base charge to rent a bike is $4.00 and the additional hourly charge for the bike rental is $1.50 per hour. d the initial base charge to rent a bike is $4.00 and the additional hourly charge for the bike rental is $2.00 per hour.

Explanation:

Step1: Identify initial value

When $x = 0$, $y=4$. So the initial - base charge (when no hours of rental have occurred) is $\$4$.

Step2: Calculate rate of change

The rate of change (slope $m$) is calculated using the formula $m=\frac{y_2 - y_1}{x_2 - x_1}$. Let's take two points, say $(1,5.5)$ and $(0,4)$. Then $m=\frac{5.5 - 4}{1-0}=\frac{1.5}{1}=1.5$. The rate of change represents the additional hourly charge, which is $\$1.50$ per hour.

Answer:

C. The initial base charge to rent a bike is $\$4.00$ and the additional hourly charge for the bike rental is $\$1.50$ per hour