Question

The parks department is monitoring level of a lake the change in water level of the lake is modeled by a third degree polynomial function P(x)

A) what do the x-values when P(x)=0 tell you about the real world situation?


I’m just really confused on what is being asked.

Answer 1

Consider a polynomial of degree 3,P(x)=0, whose roots are
`x_(1),x_(2),x_(3)`.

It means whether temperature remains constant or there is rise in temperature or temperature decreases the volume of water in lake decreases. it can't increase because if you think temperature is constant chances are you can say surely that earth may soak water.

So, if
`x_(1),x_(2),x_(3)` are roots of the polynomial P(x)=0, it means with increase in day water level of pond is decreasing.

Consider,
`x_(1)\leq x_(2)\leq x_(3)`, then

`x_(1)`= Level of water in the pond on
`x_(1)` th day.=
`V_(1)`

`x_(2)`= Level of water in the pond on
`x_(2)` th day.=
`V_(2)`

`x_(3)`= Level of water in the pond on
`x_(3)` rd day.=
`V_(3)`

`V_(3)< V_(2)< V_(1)`