Question

the r value is 0.2 per year. what percentage growth rate would the population show in the absence of constraints? (round your answer to the nearest whole number.)

Answer 1

The percentage  growth rate would the population show in the absence of constraints is 22%

A logistic model is modeled by the function

N = K/1+be^rt

where, the constant k represents carrying capacity,

the constant b is formed by b = k/n(o) - 1

the value of r will be the intrinsic exponential growth rate and t represent time.

⇒ If there is no limiting factors, then the logistic model would be exponential according to formula:

N = N(0)e^rt

Since the corresponding growth factor for this exponential function is a = e^r

so the variable r can be obtained from a using :

r = ln a

a = e^r

given r= 0.2

a = ?

a = e°·²

a = 1.221

a = 1.22

⇒ 1.22 -  1 = 0.22

0.22×100 = 22%

Hence we get the percentage growth as 22%.

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