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I have a logistic growth equation for a population where K = 820 carrying capacity, and...

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I have a logistic growth equation for a population where K = 820carrying capacity, and P(0) =550 initial population with a growthrate r of 0.25. Using the equation P= K/(1+A.e^-rt) i can find outthe Value of A from initial conditions as A=(K-P(0))/P(0) and applythe equation to calculate values of P at different time intervalsbetween 0 ans 12 years. If I have to use the same parameters as alogistic decay starting with an initial population of 820 and afinal population of 550, what would be the value of A. If I applyinitial conditions then the value of A comes as negative and if weuse -r as negative growth rate in the exponent of the denominator,there result does not follow a logistic decay. However if we keep Apositive and r negative then we get a logistic decay. Can youplease clarify this confusion.

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