Answer:
Explanation: In 1991, the moose population in a park was measured to be 3490. By 1996, the population was measured again to be 4090. If the population continues to change linearly:
If the moose population continues to change linearly, we can estimate the population at any given year by assuming a constant rate of change. To do this, we'll first calculate the rate of change per year based on the data provided.
The population increased from 3490 in 1991 to 4090 in 1996, which represents a change of 4090 - 3490 = 600 moose over a span of 1996 - 1991 = 5 years.
The rate of change per year can be calculated by dividing the change in population by the number of years:
Rate of change = Change in population / Number of years
= 600 moose / 5 years
= 120 moose per year
Now that we have the rate of change, we can estimate the population for any given year using the linear model.
Let's say we want to estimate the moose population in the year 2023. We need to determine the number of years that have passed since 1991, which is 2023 - 1991 = 32 years.
To calculate the estimated population, we multiply the number of years by the rate of change and add it to the initial population in 1991:
Estimated population in 2023 = Initial population in 1991 + (Rate of change × Number of years)
= 3490 + (120 moose per year × 32 years)
= 3490 + 3840
= 7330
Therefore, based on a linear model, the estimated moose population in the year 2023 would be 7330. Keep in mind that this is an estimation based on the assumption of a constant rate of change, and actual population dynamics can be more complex.