+0  
 
0
1344
1
avatar

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

Guest Mar 5, 2015

Best Answer 

 #1
avatar+17711 
+5

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.

geno3141  Mar 5, 2015
Sort: 

1+0 Answers

 #1
avatar+17711 
+5
Best Answer

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.

geno3141  Mar 5, 2015

17 Online Users

avatar
avatar
avatar
avatar
We use cookies to personalise content and ads, to provide social media features and to analyse our traffic. We also share information about your use of our site with our social media, advertising and analytics partners.  See details