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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).
check_circleAnswer
Step 1

Given:

‘t’ is measured in the year.

Here, the equation of the logistic growth model:

2500
n(t)
0.5 24.5e0044
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2500 n(t) 0.5 24.5e0044

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Step 2

Part (a)

Finding the initial population of bird:

Here, t = 0

2500
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
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2500 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

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Step 3

Part (b)

The graph of the funct...

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10000 5000 3000 5000 1000 2000 4000 6000 -1000 7000 -5000 10000

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Tagged in

Math

Calculus

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