Question

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

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.

Answer 1

To understand the reproduction of Lori's goldfish, we need to analyze the rate of reproduction. A 32 percent increase each month means that the population of fish will grow by a factor of 1.32 (100% + 32% = 132%, or 1.32 in decimal form).

Given this, let's evaluate the provided statements:

1. **The points on the graph will have a common ratio of 32.** - This is incorrect because a common ratio of 32 would imply that the population grows by a factor of 32 each month, which is not the case.

2. **The graph will begin with the point (1,5) because Lori starts with five fish.** - This statement is incorrect; it should start with the point (0,5) because at month 0 (the starting point), she has 5 fish.

3. **The graph will have a constant rate of change.** - This statement is incorrect; since the fish population increases by a percentage, the growth is exponential, not linear. Therefore, there isn’t a constant rate of change.

4. **The points on the graph will have a common ratio of 1.32.** - This statement is correct. Since the fish reproduce at a rate of 32% each month, the population will increase by a factor of 1.32 each month.

Based on the analysis, the correct statement that discusses a key feature of the graph of this situation is:

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