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.

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

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.