Question

keisha rents a scooter to get to the beach. the rental company charges $2 per mile plus a fee of $20. donovan rents a bike to get to the beach. the equation below shows the cost in dollars, y, as a function of the miles donovan travels, x. compare the rates of change of the two functions. donovan: y = x + 28 keisha’s rental costs $\square$ per mile. donovan’s rental costs $?$ per mile. the rate of change of keisha’s function is $?$ the rate of change of donovan’s function.

Explanation:

Step1: Analyze Keisha's cost function

Keisha's rental cost: The company charges $2 per mile plus a $20 fee. So her cost function is \( y = 2x + 20 \), where the coefficient of \( x \) (miles) is the cost per mile. So Keisha's cost per mile is $2.

Step2: Analyze Donovan's cost function

Donovan's cost function is \( y = x + 28 \). In the slope - intercept form \( y=mx + b \) (where \( m \) is the slope, representing the rate of change), the coefficient of \( x \) is 1. So Donovan's cost per mile is $1.

Step3: Compare the rates of change

Keisha's rate of change (cost per mile) is 2, Donovan's is 1. So the rate of change of Keisha's function is greater than the rate of change of Donovan's function.

Answer:

Keisha’s rental costs $\boldsymbol{2}$ per mile. Donovan’s rental costs $\boldsymbol{1}$ per mile. The rate of change of Keisha’s function is $\boldsymbol{\text{greater than}}$ the rate of change of Donovan’s function.