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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.

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

Niall rents a bike for $20 per hour.

Answer 1

To analyze which of the situations could describe the concave-up, increasing curve, we need to look at the characteristics of each option:

1. Sienna buys a vintage record for $20. Its value appreciates by 20 percent each year.
   This situation represents exponential growth, as the value of the record increases by a percentage of its current value each year. The graph would be concave-up and increasing.

2. Juveldy puts $20 in a high-yield savings account. His investment triples every year.
   This is also exponential growth, and the value of the investment grows significantly each year. The graph would be concave-up and increasing.

3. There are 200 cockroaches in a building, and the population triples every day.
   Similarly, this represents exponential growth. The population of cockroaches increases very rapidly each day, leading to a concave-up, increasing graph.

4. Niall rents a bike for $20 per hour.
   This situation does not describe growth, only a fixed cost increasing linearly as time goes on. The graph would not be concave-up; instead, it would be a straight line at a constant rate.

Based on this analysis, the situations that could describe the concave-up, increasing curve are:

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

Given the context, any of the first three situations could represent the described graph, but the best matches would be those indicating exponential growth.