Which of the following situations could describe the graph?

Juveldy puts $20 in a high-yield savings account. His investment triples every year.
Sienna buys a vintage record for $20. Its value appreciates by 20 percent each year.
Niall rents a bike for $20 per hour.
There are 200 cockroaches in a building, and the population triples every day.

1 answer

To determine which situation corresponds to a specific type of graph, let's analyze each option:

  1. Juveldy puts $20 in a high-yield savings account. His investment triples every year.
    This situation describes exponential growth because the investment triples, which is a multiplication by a constant factor (3). The value of the investment can be expressed as \( V(t) = 20 \cdot 3^t \), where \( t \) is the number of years. This graph would show a rapidly increasing curve (exponential growth).

  2. Sienna buys a vintage record for $20. Its value appreciates by 20 percent each year.
    This situation also describes exponential growth, but at a different rate. The value can be expressed as \( V(t) = 20 \cdot (1.2)^t \), where \( t \) is the number of years. The graph would show an increasing curve, but not as steep as Juveldy's investment.

  3. Niall rents a bike for $20 per hour.
    This situation represents a linear relationship, as the cost increases by a fixed amount ($20) for each hour that passes. The graph of this scenario would be a straight line with a slope corresponding to the hourly rate.

  4. There are 200 cockroaches in a building, and the population triples every day.
    Similar to Juveldy's investment, this scenario also describes exponential growth because the population triples daily. The value can be expressed as \( P(t) = 200 \cdot 3^t \), where \( t \) is the number of days. This graph would show a steep upward curve.

Summary:

  • Exponential growth (tripling): Juveldy and the cockroach population.
  • Exponential growth (20% increase): Sienna.
  • Linear growth (fixed rate): Niall.

If you're attempting to identify a specific graph, you should consider the characteristics of each situation described, focusing particularly on whether they illustrate exponential growth (curved graph) or linear growth (straight line). If you have a specific graph to analyze, compare its shape with these descriptions.