# A population is modeled by the differential equation

step by step solution:

Let the function be

P=f(t)

We know that for a increasing function,

First derivative of a function should be strictly greater than zero:

Therefore, For an increasing function P

\frac{dP}{dt}\gt 0~~~~~~where~~ ~,\frac{dP}{dt}=1.7P(1-\frac{P}{6000})

Substitute the value of dp/dt into the given inequality we get

\textcolor{primary}{1.7P(1-\frac{P}{6000})}\gt 0

Using distributive property we get

(\textcolor{primary}{1.7P}\times 1-\textcolor{primary}{1.7P}\times \frac{P}{6000})\gt 0

Solve the inequality for P:

1.7p(1-\frac{p}{6000})>0
p(1-\frac{p}{6000})>0
p(6000-p)>0

hence we can conclude that p is:

0\lt P\lt 6000

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