Koala Bear Population Limits and Growth: A Mathematical Analysis

[Jan Hill]

Homework Statement

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

Homework Equations

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.

 

[Jan Hill]

Thank you