Question

Which of the following situations could describe the graph? (1 point) Responses Sienna buys a vintage record for $20. Its value appreciates by 20 percent each year. Sienna buys a vintage record for $20. Its value appreciates by 20 percent each year. Niall rents a bike for $20 per hour. Niall rents a bike for $20 per hour. Juveldy puts $20 in a high-yield savings account. His investment triples every year. Juveldy puts $20 in a high-yield savings account. His investment triples every year. There are 200 cockroaches in a building, and the population triples every day.
Graph :
First point-(0,20)
Second point-(1,60)
Third point-(2,180)
Fourth point-(3,540)

Answer 1

To identify which situation describes the graph, let's analyze the growth of the values in the graph.

The points on the graph represent the following values:

- At year 0, the value is 20.
- At year 1, the value is 60.
- At year 2, the value is 180.
- At year 3, the value is 540.

Now, let's determine the growth between each point:

1. **From (0, 20) to (1, 60)**:
- Increase: 60 - 20 = 40
- Growth rate: 40 / 20 = 2 (200% increase)

2. **From (1, 60) to (2, 180)**:
- Increase: 180 - 60 = 120
- Growth rate: 120 / 60 = 2 (200% increase)

3. **From (2, 180) to (3, 540)**:
- Increase: 540 - 180 = 360
- Growth rate: 360 / 180 = 2 (200% increase)

This shows that the value is tripling every time interval (it grows by a factor of 3):

- After 1 unit of time: \( 20 \times 3 = 60 \)
- After 2 units of time: \( 60 \times 3 = 180 \)
- After 3 units of time: \( 180 \times 3 = 540 \)

Now, let's review the provided situations:

1. **Sienna buys a vintage record for $20. Its value appreciates by 20 percent each year.**
- This would not fit as the growth is not by a factor of 3.

2. **Niall rents a bike for $20 per hour.**
- This represents a constant price and does not match the growth pattern.

3. **Juveldy puts $20 in a high-yield savings account. His investment triples every year.**
- This fits perfectly with the graph’s growth pattern (tripling).

4. **There are 200 cockroaches in a building, and the population triples every day.**
- This represents a similar type of exponential growth, but it starts at 200, not 20.

The correct situation that matches the graph is:

**Juveldy puts $20 in a high-yield savings account. His investment triples every year.**