Question 1134613: A scientist studied the number of bears in a certain area. In 2010, there were 42 bears, and in 2012, there were 67 bears. Based on a linear model, how many bears will be in that area in 2016?
Found 3 solutions by Glaviolette, MathTherapy, greenestamps:
Answer by Glaviolette(140)   (Show Source):
Answer by MathTherapy(10552)  (Show Source):
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A scientist studied the number of bears in a certain area. In 2010, there were 42 bears, and in 2012, there were 67 bears. Based on a linear model, how many bears will be in that area in 2016?
Let 2010 be year 0. Then 2012 and 2016 are 2, and 6 years, respectively
We then get the 2 points, (0, 42) and (2, 67)
Applying the slope (m) formula using the 2 points above, we get: m, or slope = 12.5
We then get the following equation using the POINT-SLOPE formula, and the point (0, 42): 
 ------ Substituting 6 (number of years since 2010) for x
Answer by greenestamps(13200)  (Show Source):
You can put this solution on YOUR website!
If you are solving the problem using formal algebra, definitely don't use 2010 and 2012 as the x values of the two data points; it just means you are going to be using MUCH larger numbers in your calculations. And in some similar problems it greatly reduces the accuracy of your answer.
Instead, use 2010 as your "reference point" and use x values of 0 and 2 (number of years after the reference point).
But you should be able to solve this problem easily without formal algebra (unless, of course, an algebraic solution is required).
In 2 years from 2010 to 2012 the population increased by 25, from 42 to 67. If the increase is linear, then in another 4 years the population will increase by 50; 67+50 = 117.
Solving the problem using formal algebra is good practice; but solving a problem using logical reasoning is excellent exercise for the brain.
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