Time (years) Bear Population
1 6
20 120
60 240
One biologist claimed that the bear population was proportionally related to the number of years after they were reintroduced into the wild. Based on the information in the table, would you agree?
No, I would not agree with the biologist's claim that the bear population is proportionally related to the number of years after they were reintroduced into the wild.
A proportional relationship means that there is a constant ratio between the two variables being studied. In this case, if the bear population were proportionally related to the number of years, we would expect to see a consistent ratio between the bear population and the number of years.
However, looking at the data in the table, we can see that the bear population does not have a consistent ratio with the number of years. For example, in the first year, there are 6 bears, but after 20 years, the population increases to 120 bears, and after 60 years, it further increases to 240 bears.
This inconsistent ratio indicates that the bear population is not proportionally related to the number of years.
To determine if the bear population is proportionally related to the number of years after reintroduction, we can calculate the ratio of the bear population to the number of years for each data point:
For the first data point (1 year, 6 bears): The ratio is 6/1 = 6.
For the second data point (20 years, 120 bears): The ratio is 120/20 = 6.
For the third data point (60 years, 240 bears): The ratio is 240/60 = 4.
Since the ratios are not consistent, we can conclude that the bear population is not proportionally related to the number of years after they were reintroduced into the wild. Therefore, I would not agree with the biologist's claim based on the information in the table.
To determine if the bear population is proportionally related to the number of years after they were reintroduced into the wild, we need to compare the ratios of the bear population to the number of years for different time periods.
Let's calculate the ratio for the first and second time period:
For the first time period (1 year):
Bear population = 6
Number of years = 1
Ratio = 6/1 = 6
For the second time period (20 years):
Bear population = 120
Number of years = 20
Ratio = 120/20 = 6
The ratios for both time periods are equal, which suggests that the bear population is proportionally related to the number of years after their reintroduction into the wild.
To further verify, let's calculate the ratio for the third time period (60 years):
Bear population = 240
Number of years = 60
Ratio = 240/60 = 4
Since the ratio for the third time period is not equal to the ratios for the previous time periods, it indicates that the bear population is not proportionally related to the number of years after reintroduction into the wild.
Therefore, based on the information in the table, we would not agree with the biologist's claim that the bear population is proportionally related to the number of years after reintroduction.