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? Explain your answer.
: Time (years) Bear Population
1 6
20 120
60 240
Based on the information in the table, it appears that the bear population is not proportionally related to the number of years after they were reintroduced into the wild.
If the bear population was proportionally related to the number of years, we would expect to see a consistent increase in the population with each passing year. However, the data in the table does not show a consistent pattern.
After the first year, the bear population increased from 6 to 120 in 20 years. This is a significant increase, indicating a rapid population growth. However, in the following 40 years, the bear population only increased by 120 more bears, reaching 240.
This irregular growth pattern suggests that there are other factors influencing the population growth or that the relationship between years and bear population is not purely proportional.
To determine whether the bear population is proportionally related to the number of years after they were reintroduced into the wild, we can calculate the population growth rate over time.
First, we need to calculate the growth rate per year by dividing the change in population by the change in time. Let's calculate the growth rate between year 1 and year 20:
Population change = 120 - 6 = 114
Time change = 20 - 1 = 19
Growth rate = Population change / Time change = 114 / 19 = 6
Now, let's calculate the growth rate between year 20 and year 60:
Population change = 240 - 120 = 120
Time change = 60 - 20 = 40
Growth rate = Population change / Time change = 120 / 40 = 3
As we can see, the growth rate between year 1 and year 20 is 6, while the growth rate between year 20 and year 60 is 3. The growth rate is not constant, indicating that the bear population is not proportionally related to the number of years after reintroduction.
Therefore, based on the given data, it is not accurate to claim that the bear population is proportionally related to the number of years after they were reintroduced into the wild.
To determine if the bear population is proportionally related to the number of years after they were reintroduced into the wild, we need to examine the data in the table.
In this case, we can compare the change in bear population with the change in time. To do this, let's calculate the proportion of the bear population for each time interval.
For the time interval from 1 year to 20 years, we can find the proportion of the bear population by dividing the population at 20 years by the population at 1 year: 120 / 6 = 20.
For the time interval from 20 years to 60 years, we divide the population at 60 years by the population at 20 years: 240 / 120 = 2.
Comparing these proportions, we can see that the proportion of the bear population does not remain constant over time. In the first time interval, the population proportion increases by a factor of 20, whereas in the second time interval, the population proportion increases by a factor of 2. This indicates that the bear population is not proportionally related to the number of years after they were reintroduced into the wild.
Therefore, based on the data in the table, I would not agree with the biologist's claim that the bear population is proportionally related to the number of years after reintroduction into the wild.