The population of a certain species of bird is limited by the type of habitat required for nesting. The population behaves according to the logistic growth model n(t) = 5600 / 0.5 + 27.5e^(-0.044t) where t is measured in years (a) Find the initial bird population. _____ birds (b)What size does the population approach as time goes on? _____ birds
+23246 To find the initial amount, replace t with 0 and solve.
To find what the population approaches, replace t with some large numbers, such as 1000 and 2000, and see what the answer approaches.
Another way to see what the population approaches is to check what happens when t becomes very large:
when t becomes very large, the expression -0.044t becomes a large negative number; but since it's an exponent, the expression e^(-0.044t) becomes very small, almost zero. When e^(-0.044t) becomes zero, 27.5e^(-0.044t) becomes zero, so the total value becomes 5600/0.5 + 0, or 11,200.
+23246 To find the initial amount, replace t with 0 and solve.
To find what the population approaches, replace t with some large numbers, such as 1000 and 2000, and see what the answer approaches.
Another way to see what the population approaches is to check what happens when t becomes very large:
when t becomes very large, the expression -0.044t becomes a large negative number; but since it's an exponent, the expression e^(-0.044t) becomes very small, almost zero. When e^(-0.044t) becomes zero, 27.5e^(-0.044t) becomes zero, so the total value becomes 5600/0.5 + 0, or 11,200.
