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.

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.

Niall rents a bike for $20 per hour.
Niall rents a bike for $20 per hour.

There are 200 cockroaches in a building, and the population triples every day.

Answer 1

choose one

Answer 2

To determine which of the situations could describe a specific type of graph, let's summarize the potential growth patterns of each option:

1. **Sienna buys a vintage record for $20. Its value appreciates by 20 percent each year.**
- This describes exponential growth. The value increases by a constant percentage each year, resulting in a curve that rises gradually. This is often modeled by the equation \(V(t) = 20(1.2)^t\), where \(V(t)\) is the value at time \(t\).

2. **Juveldy puts $20 in a high-yield savings account. His investment triples every year.**
- This also describes exponential growth but at a faster rate than Sienna's record. The investment triples, which can be represented by the equation \(I(t) = 20(3)^t\). This results in a steeply rising curve.

3. **Niall rents a bike for $20 per hour.**
- This is a linear situation, where the cost (or value) increases linearly based on time but does not exhibit exponential growth. Therefore, this would produce a straight line, rather than a curve.

4. **There are 200 cockroaches in a building, and the population triples every day.**
- Similar to Juveldy's case, this is also an example of exponential growth, where the population triples each day, represented by the equation \(P(t) = 200(3)^t\). This would lead to a very steep growth graph.

Given these descriptions, options 1, 2, and 4 exhibit exponential growth, while option 3 exhibits linear growth. The situations that "could describe the graph" of exponential growth are:

- Sienna's vintage record (option 1)
- Juveldy's savings account (option 2)
- The cockroach population (option 4)

If you're looking for exponential growth specifically, options 1, 2, and 4 fit that criteria.

Answer 3

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

This situation illustrates a clear example of exponential growth, as the investment triples each year, resulting in rapid and significant increases over time.