(a) The initial bird population can be found by setting t = 0 in the given logistic growth model.

n(t) = 2,600/(0.5 + 25.5e^(-0.041*0))

When t = 0, e^0 = 1. So,

n(0) = 2,600/(0.5 + 25.5*1)
n(0) = 2,600/26
n(0) = 100

So, the initial bird population is 100 birds.

(b) To draw a graph of the function n, you would need to plot the function n(t) = 2,600/(0.5 + 25.5e^(-0.041t)) over a range of t values. This can be done using graphing software or a graphing calculator. The graph will start at the initial population of 100 birds and will show how the bird population changes over time according to the logistic growth model. The graph will have an S-shape, characteristic of logistic growth models, showing initial exponential growth followed by a slowing of growth as the population approaches its carrying capacity.

Question

(a) The initial bird population can be found by setting t = 0 in the given logistic growth model.

n(t) = 2,600/(0.5 + 25.5e^(-0.041*0))

When t = 0, e^0 = 1. So,

n(0) = 2,600/(0.5 + 25.5*1)
n(0) = 2,600/26
n(0) = 100

So, the initial bird population is 100 birds.

(b) To draw a graph of the function n, you would need to plot the function n(t) = 2,600/(0.5 + 25.5e^(-0.041t)) over a range of t values. This can be done using graphing software or a graphing calculator. The graph will start at the initial population of 100 birds and will show how the bird population changes over time according to the logistic growth model. The graph will have an S-shape, characteristic of logistic growth models, showing initial exponential growth followed by a slowing of growth as the population approaches its carrying capacity.

Knowee AI · Accepted Answer

(a) The initial bird population can be found by setting t = 0 in the given logistic growth model.

n(t) = 2,600/(0.5 + 25.5e^(-0.041*0))

When t = 0, e^0 = 1. So,

n(0) = 2,600/(0.5 + 25.5*1)
n(0) = 2,600/26
n(0) = 100

So, the initial bird population is 100 birds.

(b) To draw a graph of the function n, you would need to plot the function n(t) = 2,600/(0.5 + 25.5e^(-0.041t)) over a range of t values. This can be done using graphing software or a graphing calculator. The graph will start at the initial population of 100 birds and will show how the bird population changes over time according to the logistic growth model. The graph will have an S-shape, characteristic of logistic growth models, showing initial exponential growth followed by a slowing of growth as the population approaches its carrying capacity.

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) = 2,6000.5 + 25.5e−0.041twhere t is measured in years.(a) Find the initial bird population. birds(b) Draw a graph of the function n

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