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Answer :
Final answer:
The number of rabbits in the range 9 years from 1990 can be determined using the exponential growth formula N = N0 * (1 + r)^t. With an initial population of 100 in 1990 and 200 in 1993, we can solve for the growth rate r and the number of time periods t. Plugging in the values, the estimated population 9 years from 1990 is approximately 252 rabbits.
Explanation:
To find the number of rabbits in the range 9 years from 1990, we need to determine the growth rate of the rabbit population. Since the population follows exponential growth, we can use the formula:
N = N0 * (1 + r)^t,
where N is the final population, N0 is the initial population, r is the growth rate, and t is the number of time periods. Given that the population was 100 in 1990 and 200 in 1993, we can identify N0 as 100 and N as the unknown value to be determined. We need to find the growth rate r and the number of time periods t.
The tagged rabbits in 1990 represent the initial population, so N0 = 100. In 1993, the population had doubled to 200, so N = 100 * (1 + r)^3 = 200. Solving for (1 + r)^3 = 2, we find that 1 + r = 2^(1/3). Therefore, r = 2^(1/3) - 1.
Since we want to find the population 9 years from 1990, t = 9. Plugging in the values, we have N = 100 * (1 + (2^(1/3) - 1))^9. Evaluating this expression gives us a final population of approximately 252 rabbits.
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