We have $3$ pieces of information about the earning of a savings account. We will write a piece-wise function that models the earning and we will graph the function piece by piece. Let's start!

First Piece

The first piece of information is the following.

The account earns 1.4 % simple interest for balances of $ 100 or less .

In this case, since the interest states the rate of change in the balance, we will consider it as a slope. If

x

represents the balance and

y = f (x)

represents the interest paid, we can write the following function. Notice that, the amount of interest is

$ 0

for

$ 0

balance. Therefore, the

y -

intercept will be

0 .

f (x) = 0.014 x if 0 \leq x \leq 100

Next, we will find the end points of our function to graph it.

$x$	Function	Substitution	$y = f (x)$
$0$	$f (x) = 0.014 x$	$f (0) = 0.014 \cdot 0$	$0$
$100$	$f (x) = 0.014 x$	$f (100) = 0.014 \cdot 100$	$1.4$

Now, we can graph the first piece of our function using the endpoints

(0, 0)

and

(100, 1.4)

. We will show the endpoints with closed points since they are included in the solution set.

Exercise