To determine which situation could describe the graph with the points (0,20), (1,60), (2,180), and (3,540), we need to analyze the growth pattern represented by those coordinates.
From the points provided:
- At \(x = 0\), the value is \(20\).
- At \(x = 1\), the value is \(60\).
- At \(x = 2\), the value is \(180\).
- At \(x = 3\), the value is \(540\).
We can see that the values increase in a manner consistent with exponential growth. To confirm this, we can examine the ratio of consecutive values:
- From \(20\) to \(60\): \(60 / 20 = 3\)
- From \(60\) to \(180\): \(180 / 60 = 3\)
- From \(180\) to \(540\): \(540 / 180 = 3\)
The ratio of each consecutive pair is \(3\), which indicates that the investment is tripling each year.
Now, let's compare this with the provided situations:
-
Juveldy puts $20 in a high-yield savings account. His investment triples every year.
This situation matches the growth pattern perfectly, as it describes an initial amount of $20 that follows the same tripling pattern. -
There are 200 cockroaches in a building, and the population triples every day.
Although this also describes a tripling growth pattern, it starts from 200, not 20. So, while it could potentially fit a similar graph shape, it does not match the specific starting value at \(x = 0\). -
Sienna buys a vintage record for $20. Its value appreciates by 20 percent each year.
This describes a linear growth pattern, not tripling, and would not produce the given points. -
Niall rents a bike for $20 per hour.
This situation suggests a constant rate, unrelated to growth patterns.
Given the reasons above, the correct response that matches the graph is:
Juveldy puts $20 in a high-yield savings account. His investment triples every year.