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?
A. The points on the graph will have a common ratio of 1.32.
B. The graph will begin with the point (1, 5) because Lori starts with five fish.
C. The points on the graph will have a common ratio of 32.
D. The graph will have a constant rate of change.
A. The points on the graph will have a common ratio of 1.32.
B. The graph will begin with the point (1, 5) because Lori starts with five fish.
C. The points on the graph will have a common ratio of 32.
D. The graph will have a constant rate of change.
Answers
GPT-4o mini
To analyze the situation, let's break down the points:
- Lori begins with 5 goldfish. This is her initial quantity.
- The reproduction rate is given as 32 percent per month. In terms of growth factor, this means each month the number of goldfish will increase by 32%. Therefore, the total number of goldfish will be multiplied by 1.32 each month.
- This indicates an exponential growth scenario, where the growth is not linear but rather multiplicative.
Now let's evaluate the statements:
A. The points on the graph will have a common ratio of 1.32. **(This is true because the population increases by 32%, which means it is multiplied by 1.32 each month.)**
B. The graph will begin with the point (1, 5) because Lori starts with five fish. **(This is incorrect since the graph should start at (0, 5) if we're using a month count starting at zero.)**
C. The points on the graph will have a common ratio of 32. **(This is incorrect. The ratio is 1.32, not 32.)**
D. The graph will have a constant rate of change. **(This is incorrect as well. The rate of change is not constant; it's exponential, meaning the increase is not the same every month but grows larger as the number of fish increases.)**
Given this analysis, the best answer is:
**A. The points on the graph will have a common ratio of 1.32.**
- Lori begins with 5 goldfish. This is her initial quantity.
- The reproduction rate is given as 32 percent per month. In terms of growth factor, this means each month the number of goldfish will increase by 32%. Therefore, the total number of goldfish will be multiplied by 1.32 each month.
- This indicates an exponential growth scenario, where the growth is not linear but rather multiplicative.
Now let's evaluate the statements:
A. The points on the graph will have a common ratio of 1.32. **(This is true because the population increases by 32%, which means it is multiplied by 1.32 each month.)**
B. The graph will begin with the point (1, 5) because Lori starts with five fish. **(This is incorrect since the graph should start at (0, 5) if we're using a month count starting at zero.)**
C. The points on the graph will have a common ratio of 32. **(This is incorrect. The ratio is 1.32, not 32.)**
D. The graph will have a constant rate of change. **(This is incorrect as well. The rate of change is not constant; it's exponential, meaning the increase is not the same every month but grows larger as the number of fish increases.)**
Given this analysis, the best answer is:
**A. The points on the graph will have a common ratio of 1.32.**