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## Homework Statement

A population [tex]x[/tex] has growth as such: [tex]x'=rx(1-\frac{x}{k})-\lambda[/tex] where [tex]r>0, k>0, \lambda\in{\textbf{R}}[/tex]. That is, r is the growth rate, k is the carrying capacity and [tex]\lambda[/tex] is a removal rate.

For what value of [tex]\lambda[/tex] is the population guaranteed to go extinct?

## Homework Equations

## The Attempt at a Solution

I've been trying to "solve the equation" so that [tex]x'=0[/tex] but then I can only find the trivial solution from this, that is, x=0.

Any ideas?