Lori buys five goldfish for her tank. Her research shows that they will reproduce at a rate of 32 percent each month. Which statement discusses a key feature of the graph of this situation?(1 point)

Responses

The points on the graph will have a common ratio of 32.
The points on the graph will have a common ratio of 32.

The graph will have a constant rate of change.
The graph will have a constant rate of change.

The points on the graph will have a common ratio of 1.32.
The points on the graph will have a common ratio of 1.32.

The graph will begin with the point (1,5) because Lori starts with five fish.

1 answer

To discuss a key feature of the graph of Lori's goldfish situation, we need to consider the initial amount of goldfish and how they reproduce.

Lori starts with 5 goldfish, and they reproduce at a rate of 32% each month. This means that each month, the population of goldfish increases by 32% of the current population.

This situation can be modeled with an exponential growth function, where the population of goldfish after each month can be expressed as:

\[ P(t) = P_0 \times (1 + r)^t \]

Where:

  • \( P(t) \) is the population at time \( t \),
  • \( P_0 \) is the initial population (5 goldfish),
  • \( r \) is the growth rate (0.32), and
  • \( t \) is the time in months.

Given these considerations, the key feature of the graph is:

The points on the graph will have a common ratio of 1.32.

This is because each month, the population multiplies by \( 1 + r = 1 + 0.32 = 1.32 \). Therefore, the correct statement is:

The points on the graph will have a common ratio of 1.32.