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:
-
From (0, 20) to (1, 60):
- Increase: 60 - 20 = 40
- Growth rate: 40 / 20 = 2 (200% increase)
-
From (1, 60) to (2, 180):
- Increase: 180 - 60 = 120
- Growth rate: 120 / 60 = 2 (200% increase)
-
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:
-
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.
-
Niall rents a bike for $20 per hour.
- This represents a constant price and does not match the growth pattern.
-
Juveldy puts $20 in a high-yield savings account. His investment triples every year.
- This fits perfectly with the graph’s growth pattern (tripling).
-
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.