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Derivatives of Exponential & Logarithmic Functions
4. Derivatives of Exponential & Logarithmic Functions / Derivatives of Exponential & Logarithmic Functions / Problem 4
Problem 4

In a newly established wildlife reserve, 100100 rabbits are introduced into an area with an estimated carrying capacity of 10,00010,000 rabbits. A logistic model of the rabbit population is given by R(t)=1,000,000100+9900e0.3tR(t) = \frac{1,000,000}{100 + 9900 e^{-0.3t}}, where tt is measured in years. How fast (in rabbits per year) is the population growing at t=0t=0? Approximate to the nearest whole number.

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