# Population and limits

#### Jan Hill

1. The problem statement, all variables and given/known data
The population of koala bears within a nature reserve at time t is greater than or equal to 0 is given by the function
N(t) = 200t/4 + t

Determine a)the lim as t-->infinity (the limiting population size)

b)when the population is exactly half of its limiting size

2. Relevant equations

3. The attempt at a solution
I don't really know where to start

#### HallsofIvy

I assume you mean N(t)= 200t/(4+ t). What you wrote does not have a limiting value.

To find the limit, divide both numerator and denominator by t:
N(t)= 200/(4/t+ 1). Now, as t goes to "infinity" (as t gets large), that "4/t" goes to 0 and what remains is the limit.

Now that you know that limiting size,set 200t/(4+ t) equal to half that number and solve for t.

Thank you

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