  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 modeln(t) =2,5000.5 + 24.5e−0.044twhere t is measured in years.(a) Find the initial bird population.(b) Draw a graph of the function n(t).

Question

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) =
 2,500 0.5 + 24.5e−0.044t

where t is measured in years.

(a) Find the initial bird population.
(b) Draw a graph of the function n(t).
Step 1

Given:

‘t’ is measured in the year.

Here, the equation of the logistic growth model:

Step 2

Part (a)

Finding the initial population of bird:

Here, t = 0 help_outlineImage Transcriptionclose2500 nt)5+24.5e04f 2500 п(0) %3 0.5+24.5e.044«0° 2500 п(0) - 0.5+24.5e 2500 п(0) 0.5 24.5x1 2500 n(0)= 0.5 24.5 n(0)2500 25 n(0)=100 fullscreen
Step 3

Part (b)

The graph of the funct... help_outlineImage Transcriptionclose10000 5000 3000 5000 1000 2000 4000 6000 -1000 7000 -5000 10000 fullscreen

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Calculus 