Question

The given model is a nonlinear function. A. True B. False

Answer 1

Answer: A. True

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Explanation:

Let x be the number of years since 1995. So x = 0 represents 0 years from 1995, x = 1 is 1 year after 1995, and so on.

The first row of the table is (x,y) = (0, 625) with y being the number of salmon.

The second row is (1, 400).

Let's find the slope of the line through these two points.

m = (y2-y1)/(x2-x1)

m = (400 - 625)/(1 - 0)

m = (-225)/1

m = -225

This tells us the salmon population dropped by 225 in the course of a year from 1995 to 1996.

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The third row shows (2, 225). Let's find the slope of the line through the two points (1, 400) and (2, 225)

m = (y2-y1)/(x2-x1)

m = (225 - 400)/(2-1)

m = (-175)/(1)

m = -175

The slope is different from the previous result. Because of this discrepancy, this means we do not have a linear model. The slope should be the same for any two points you pick from this table if you wanted a linear model.

Put another way, there is less steep a drop of the population, and the decay curve is slowly flattening out.