Question

Draw input and output diagrams for each problem and write a statement that shows how the output depends on the input.

1. The cost of renting a bicycle is $10 for the first hour and $5 for each additional hour. Write a function that represents the total cost of renting a bicycle as a function of the number of hours.

Answer 1

The input and output diagrams for the problem is added as an attachment

The equation is C(h) = 10 + 5(h − 1) or C(h) = 5 + 5h

The total cost of renting a bicycle (C) depends on the number of hours (h)

Drawing input and output diagrams for the problem

Representing the total cost of renting a bicycle as C and the number of hours as h.

The cost for the first hour is $10, and for each additional hour, the cost is $5.

So, the function representing the total cost (C) as a function of the number of hours (h) is:

C(h) = 10 + 5(h - 1)

Here,

h - 1 represents the additional hours beyond the first hour.

Expand

C(h) = 10 + 5h - 5

So, we have

C(h) = 5 + 5h

The statement that shows how the output (total cost) depends on the input (number of hours) is that

The total cost of renting a bicycle (C) depends on the number of hours (h) according to the formula C(h) = 10 + 5(h − 1)

This is so because

• The number of hours h is the independent variable
• The total cost C is the dependent variable

The input and output diagram for the problem is the graph and it is added as an attachment