Answer:
a) Current population of Glen Road = 50,000
b) Population of Glen Road in the long run = 25,000
Step-by-step explanation:
P(t) = (25t² + 125t + 200)/(t² + 5t + 40)
where P is population (in thousands) t years from now.
a) The current population of Glen Road
At the current moment, t = 0
P(0) = (25(0²) + 125(0) + 200)/((0²) + 5(0) + 40)
P(0) = (0+0+200)/(0+0+40)
P(0) = (200/40) = 50,000
b) The population in the long run
In the long run, t --> ∞
P(t) = (25t² + 125t + 200)/(t² + 5t + 40)
Divide numerator and denominator by t²
P(t) = (25 + (125/t) + (200/t²))/(1 + (5/t) + (40/t²))
As t --> ∞
P(t --> ∞) = (25 + (125/∞) + (200/∞))/(1 + (5/∞) + (40/∞))
Every number divided by infinity goes to 0.
P(t --> ∞) = (25 + 0 + 0)/(1 + 0 + 0)
P(t --> ∞) = (25/1)
P(t --> ∞) = 25,000
