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.