Use the image to answer the question.

Question

A concave-up, increasing curve is plotted on a coordinate plane. The x-axis ranges from 0 to 4 in increments of 0.1 but labeled at 0.5 intervals. The y-axis ranges from 0 to 800 in increments of 50 but labeled at intervals of 200. The curve passes through 4 marked and labeled points.

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.

Answer 1

Based on the description of the graph as a concave-up, increasing curve, we can analyze the responses to determine which situation fits this description.

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

   • This would produce an exponential growth pattern without the steep increase typical of very fast growing functions. It might be increasing but likely not as quickly as the other options.

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

   • This describes a linear situation (fixed cost per hour), resulting in a straight line rather than a concave-up curve.

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

   • This is a case of exponential growth and would lead to a very steep increase, which typically creates a concave-up curve.

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

   • Similar to Juveldy's situation, this involves exponential growth that would result in a quick rise, resulting in a concave-up curve.

Given the concave-up shape of the graph, both Juveldy's investment scenario and the cockroach population scenario fit the description. However, if we consider the rate of growth in a short time frame, the cockroach population would increase very rapidly compared to the others.

Therefore, the best fit for the description of the graph, which should imply a strong accelerating effect as seen in exponential growth, is:

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

This option magnifies the characteristics observed in the graph better than the others.