Camille receives a piggy bank containing 4 dollars for her birthday. Every week, Camille adds 8 dollars to the piggy bank. Represent this situation with a table, a graph, and an equation.

Question

Let’s start by representing this situation with a table. Start by finding the amount in the piggy bank after 0, 1, 2, and 3 weeks.
Time in weeks Dollars in the piggy bank
0
1
2
3
You got it!
Plot the points below on the coordinate plane to represent the amount in the piggy bank after 0, 1, 2, and 3 weeks.
Time in weeks Dollars in the piggy bank
0 4
1 12
2 20
3 28
Good work!
We can connect the points you just graphed with a line. To find the equation that represents this linear function, you’ll need the rate of change and the initial amount in the piggy bank. Start by finding the rate of change. In other words, by how much does the number of dollars in the piggy bank change for every week?
t
y
0
1
2
3
4
5
6
7
8
9
10
0
4
8
12
16
20
24
28
32
36
40
Time in weeks
Dollars in the piggy bank
Rate of change:

Answer 1

To find the rate of change, we need to observe how much money is added each week. According to the problem, Camille starts with 4 dollars in her piggy bank and adds 8 dollars every week.

The rate of change can be expressed as:

\[ \text{Rate of Change} = \text{Change in Dollars} / \text{Change in Time} \]

Since Camille adds 8 dollars each week, the rate of change is:

\[ \text{Rate of Change} = \frac{8 \text{ dollars}}{1 \text{ week}} = 8 \text{ dollars per week} \]

Now, we can express the situation with an equation. We know:

• The initial amount (when \( t = 0 \)) is 4 dollars.
• The amount increases by 8 dollars for every week.

The equation can be written as:

\[ y = 8t + 4 \]

Where:

• \( y \) is the total amount of dollars in the piggy bank,
• \( t \) is the number of weeks.

So, the table, graph, and equation are as follows:

Table

| Time in weeks (t) | Dollars in the piggy bank (y) | |--------------------|-------------------------------| | 0 | 4 | | 1 | 12 | | 2 | 20 | | 3 | 28 |

Graph

The graph should plot the points (0, 4), (1, 12), (2, 20), and (3, 28), which will show a straight line with a slope of 8, starting at the point (0, 4).

Equation

\[ y = 8t + 4 \]

In summary:

• Rate of change: 8 dollars per week
• Equation: \( y = 8t + 4 \)

This equation represents the amount of money in Camille's piggy bank as a function of time in weeks.