Question

Yield is the total number of fish caught each year. Maximum sustainable yield is the total number of fish you can catch without harming the population. You are given a fish population that is described by the equation y = x2 + 3 and another fish population being overfished as described by the equation y = x+ 5 where x is the number of years and y is the number of populations. Do populations ever meet? If so describe where they meet and what it means in the context of the problem.

Answer 1

So the two equations, one for the fish population and one for the fish population being overfished, are equal at the two year mark and this means that fishing would probably have to stop or reduce significantly after two years.

Explanation:

i) fish population 1 ⇒
`y_(1)` =
`x^(2)` + 3

ii) second fish population 2 ⇒
`y_(2)` = x + 5

where x is the number of years

If the populations were to meet then we would get

`x^(2)` + 3 = x + 5 ⇒
`x^(2)` - x -2 = 0 ∴ (x - 2)(x + 1) = 0 ∴ x = 2 years.

So the two equations, one for the fish population and one for the fish population being overfished, are equal at the two year mark and this means that fishing would probably have to stop or reduce significantly after two years.