Question

You are purchasing books summer reading for $4.50 each. Part A: Your total cost, C, depends on,The input is,and the output is,Part B: If you purchase 12 books, write the total cost in function notation.

Answer 1

Answer:

Part A) see the explanation

Part B) $C(12)=\ 54$

Step-by-step explanation:

Part A)

we know that

A relationship between two variables, x, and C, represent a proportional variation if it can be expressed in the form $k=\frac{C}{x}$ or $C=kx$

Let

C ---> is the total cost (represent the output or dependent variable)

x ----> is the number of books (represent the input or independent variable)

In this problem

we have a proportional relationship between the variables x and C

Part B)  we know that

The linear equation is given by

$C=kx$

The constant of proportionality k is the same that the slope or unit rate of the linear equation

In this problem the constant k is given

$k=\ 4.50\ per\ book$

so

$C=4.50x$

For x=12 books

substitute in the equation and solve for C

$C=4.50(12)=\ 54$

In function notation

$C(12)=\ 54$