In 1994 the moose population in a park was measured to be 6400. By 1996, the population was measured again to be 6800. If the population continues to change linearly:
Find an equation for the moose population, y,in terms of x, the years since 1994.
Ive been helped on getting the equation. but now the question is asking what does my equation predict for the year 2006?
6800-6400 = 400
So, the population rises by 200 each year. Go with that...
To find out what your equation predicts for the year 2006, you need to use the equation you found, which represents the linear relationship between the moose population (y) and the years since 1994 (x).
First, let's determine the rate of change in the population over the years. The population increased from 6400 in 1994 to 6800 in 1996. To find the change in population per year, we subtract the population in 1994 from the population in 1996 and then divide by the number of years between the measurements:
Change in population = (6800 – 6400) / 2 = 200 / 2 = 100
So, for every year elapsed, the moose population increases by 100.
Next, we can use this rate of change to construct the equation for the moose population (y) in terms of the years since 1994 (x):
y = mx + b
where m represents the rate of change and b is the initial population. Substituting the given values, we have:
y = 100x + 6400
Now, to find the predicted moose population for the year 2006 (12 years since 1994), substitute x = 12 into the equation:
y = 100(12) + 6400
y = 1200 + 6400
y = 7600
Therefore, the equation predicts that the moose population in the year 2006 would be 7600.