For the following exercises, use this scenario: The population P of a koi pond over x months is modeled by the function P(x) = 68/1 + 16e−0.28x.

Use the intersect feature to approximate the number of months it will take before the population of the pond reaches half its carrying capacity.

Expert Solution

Consider a logistic growth model;

P(x) = 68/(1 + 16e−0.28x)

The number of months it will take for the population for 20 koi in the population is determined as follows:

Put P = 20 as follows:

20 = 68/(1 + 16e-0.28x)

Therefore,

20(1 + 16e-0.28x) = 68

20 + 320e-0.28x = 68

320e-0.28x = 68 – 2

e-0.28x = 48/320

Take natural logarithm on both sides as follows:

ln(e-0.28x) = ln(48/320)

-0.28x = -1.897

x = -1.897/-0.28

= 6.78

Therefore, the number of months it will take for the population for 20 koi in the population is 6.78 months.

Nabeel answered 1 year ago

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