Question

the table shows the cost, y, when a bike is rented for x number of hours.
bike rentals
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: Find the initial value

The initial value is the value of \(y\) when \(x = 0\). From the table, when \(x=0\), \(y = 4\). So the initial base charge is \(\$4.00\).

Step2: Calculate the 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 \((x_1,y_1)=(0,4)\) and \((x_2,y_2)=(1,5.5)\). Then \(m=\frac{5.5 - 4}{1-0}=\frac{1.5}{1}=1.5\).

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.