Question to test your Exponential Functions knowledge

Question

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+9900e−0.3tR(t)=\frac{1,000,000}{100 + 9900 $$e^{-0.3t}$$}, where tt is measured in years. Determine the time when the population reaches 6,0006,000 rabbits. Also, find the time when the population reaches 90%90\% of the carrying capacity. Round the final answer to the nearest integer.

Accepted Answer

The time when the population reaches 6,0006,000 rabbits is approximately 17 years17	ext{ years}.The time when the population reaches 90%90\% of the carrying capacity (9,0009,000 rabbits) is approximately 23 years23	ext{ years}.

Answer

The time when the population reaches 6,0006,000 rabbits is approximately 27 years27	ext{ years}.The time when the population reaches 90%90\% of the carrying capacity (9,0009,000 rabbits) is approximately 33 years33	ext{ years}.

Answer

The time when the population reaches 6,0006,000 rabbits is approximately 23 years23	ext{ years}.The time when the population reaches 90%90\% of the carrying capacity (9,0009,000 rabbits) is approximately 17 years17	ext{ years}.

Answer

The time when the population reaches 6,0006,000 rabbits is approximately 33 years33	ext{ years}.The time when the population reaches 90%90\% of the carrying capacity (9,0009,000 rabbits) is approximately 27 years27	ext{ years}.

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