Question

David receives a piggy bank containing 3 dollars for his birthday. Every week, David adds 6 dollars to the piggy bank. Represent this situation with a table, a graph, and an equation.
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

Answer 1

Let's fill in the table with the amount of money in David's piggy bank for each specified week.

David starts with 3 dollars and adds 6 dollars each week.

- **After 0 weeks**: David has 3 dollars.

- **After 1 week**: David has 3 + 6 = 9 dollars.

- **After 2 weeks**: David has 9 + 6 = 15 dollars.

- **After 3 weeks**: David has 15 + 6 = 21 dollars.

Now we can represent this information in the table:

| Time in weeks | Dollars in the piggy bank |
|---------------|---------------------------|
| 0 | 3 |
| 1 | 9 |
| 2 | 15 |
| 3 | 21 |

Next, we can express this situation with a graph. The x-axis will represent the number of weeks, and the y-axis will represent the total dollars in the piggy bank.

The points for the graph based on the table are:
- (0, 3)
- (1, 9)
- (2, 15)
- (3, 21)

Finally, we can represent this situation with an equation. Let \( d \) be the total dollars in the piggy bank, and \( w \) be the number of weeks. The equation that represents the amount in the piggy bank after \( w \) weeks is:

\[
d = 6w + 3
\]

Where:
- \( 6w \) is the total amount added after \( w \) weeks,
- \( 3 \) is the initial amount in the piggy bank.

This fully represents the situation with a table, a graph, and an equation.