(0,20) (1.60) (2,180) (3,540)

Question

Which of the following situations could describe the graph?

(1 point)
Responses

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

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.

Answer 1

To determine which situation could describe the graph, we need to analyze the points given:

• (0, 20)
• (1, 60)
• (2, 180)
• (3, 540)

The first coordinate represents time (in years), and the second coordinate represents the value or population at that time.

Let's evaluate the options given:

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

   • This would imply exponential growth starting from 200, which does not match the initial point (0, 20).

2. Sienna buys a vintage record for $20. Its value appreciates by 20 percent each year.

   • Initially, the value is $20. After one year: $20 + (20% of $20) = $20 + $4 = $24 (not matching). This will not fit with the points provided.

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

   • This suggests a linear increase based on hours rented. It does not correspond with the exponential growth indicated by the points.

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

   • If we start with $20 and it triples:
     • Year 0: $20
     • Year 1: $20 * 3 = $60
     • Year 2: $60 * 3 = $180
     • Year 3: $180 * 3 = $540
   • This matches exactly with all given points.

Therefore, the correct response is:

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