Chapter 9.7, Problem 22PPS

To determine

The type of function of Adam’s and Suzanne’s savings account

Answer to Problem 22PPS

Adam’s monthly balance represents a linear function.

Suzanne’s monthly balance represents a non-linear function.

Explanation of Solution

Given:

Adam puts $15 in his savings account every month

Suzanne doubles her bank account balance every month

Calculation:

Linear Functions: The graph of linear functions is always a straight line. These functions have the form $y=a+bx$ .

The slope of the linear graph always remains constant. The slope of the equation is given by:

  $m=\frac{y_2-y_1}{x_2-x_1}$

Adam’s savings account’s balance for each month can be written in tabular form as:

Month (x)	Balance (y)
1	15
2	30
3	45
4	60
5	75

From the table, slope can be found as:

  $\begin{array}{l}{m}_1=\frac{30-15}{2-1}\\ m_1=\frac{15}{1}=15\\ \\ m_2=\frac{45-30}{3-2}\\ m_2=\frac{15}{1}=15\\ \\ m_3=\frac{60-45}{4-3}\\ m_3=\frac{15}{1}=15\end{array}$

As m1=m2=m3, the slope is constant, hence, Adam’s monthly balance represents a linear function.

Now, Suzanne’s savings account’s balance for each month can be written in tabular form as:

Month (x)	Balance (y)
1	y
2	2y
3	4y
4	8y
5	16y

From the table, slope can be found as:

  $\begin{array}{l}{m}_1=\frac{2y-y}{2-1}\\ m_1=\frac{y}{1}=y\\ \\ m_2=\frac{4y-2y}{3-2}\\ m_2=\frac{2y}{1}=2y\\ \\ m_3=\frac{8y-4y}{4-3}\\ m_3=\frac{4y}{1}=4y\end{array}$

As m1 is not equal to m2 is not equal to m3, the slope is not constant, hence, Suzanne’s monthly balance represents a non-linear function.