Question

One species of fish in a fishery had an initial population

of 255 fish and after 9 seasons, the population had grown to
480 fish. A second species that was being overfished started
with an initial population of 450 fish, and after the same 9
seasons, it had a new population of 90 fish. Assuming a
linear growth, write the equations for the population of
•each species. Graph your equations in the coordinate plane.
Find the point in the graph which represents when the two
populations will have the same number of fish. After how
many seasons will the second population be eliminated?

Answer 1

9514 1404 393

Answer:

• y = 25x +255
• y = -40x +450
• (3, 330)
• 11 1/4 seasons

Explanation:

The 2-point form of the equation of a line is useful for these problems. It is ...

y = (y2 -y1)/(x2 -x1)(x -x1) +y1

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a) The two points are (0, 255) and (9, 480). The equation is ...

y = (480 -255)/(9 -0)(x -0) +255

y = 25x +255

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b) The two points are (0, 450), (9, 90). The equation is ...

y = (90 -450)/(9 -0)(x -0) +450

y = -40x +450

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c) The point where both populations are the same is (3, 330).

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d) The second population will be eliminated after 11 1/4 seasons.