Question

a city tour company charges customers to rent electric scooters. the total cost includes an initial fee, which is the cost before any hours are ridden, and an additional rate for each hour the scooter is ridden. the table shows the total cost based on the number of hours ridden. which two statements accurately describe the rate of change and the initial value in this situation? a the hourly rate to rent a scooter is $5 b the hourly rate to rent a scooter is $10 c the initial fee to rent a scooter is $10 d the initial fee to rent a scooter is $5

Explanation:

Step1: Calculate the hourly rate

The rate of change (slope) \(m\) can be calculated using the formula \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Let \((x_1,y_1)=(1,15)\) and \((x_2,y_2)=(2,25)\). Then \(m=\frac{25 - 15}{2 - 1}=\frac{10}{1}=10\).

Step2: Find the initial value

Use the point - slope form \(y - y_1=m(x - x_1)\). Substitute \(m = 10\), \(x_1=1\), \(y_1 = 15\). \(y-15=10(x - 1)\), \(y-15=10x-10\), \(y = 10x+5\). When \(x = 0\) (initial value, no hours ridden), \(y=5\).

Answer:

B. The hourly rate to rent a scooter is $10; D. The initial fee to rent a scooter is $5