Question

One species of fish in a fishery had an initial population of 255 fish and grew by 25 fish each season. A second species that was being overfished started with an initial population of 450 fish, and then decreased by 40 fish each season. Assuming a linear change, write equations for the populations of each species. When will the two populations have the same amount of fish? After how many seasons will the second species be eliminated?

Answer 1

a) during the 3rd season the populations will be the same

b) after 11 1/4 seasons the second species of fish will be eliminated

Explanation:

1) y = 25x + 255

2) y = -40x + 450

the above linear equations model the statements from the problem

we can find out when the two populations will have the same amount by graphing them and finding the point of intersection or by setting them equal to each other:

25x + 255 = -40x + 450

add 40x to each side to get:

65x + 255 = 450

subtract 255 from each side to get:

65x = 195

x = 195/65

x = 3

To find the season when the second species is eliminated we can use the second equation and set 'y' equal to zero and solve for 'x':

0 = -40x + 450

subtract 450 from each side to get:

-450 = -40x

x = -450/-40

x = 11.25