It will take approximately 5 years for the rabbit population to reach 25,000.
Let's find the equation for the rabbit population over time and then determine how long it will take for the population to reach 25,000.
Equation for the rabbit population:
We can model the rabbit population using the following exponential growth equation:
P(t) = P_initial * (1 + growth_rate)^t
where:
P(t) is the rabbit population in thousands after t years
P_initial is the initial rabbit population (8000 in this case)
growth_rate is the annual growth rate (26% which is equal to 0.26)
t is the number of years that have passed
Time to reach 25,000 rabbits:
We want to find the value of t for which P(t) is equal to 25,000. So we can set up the following equation:
25000 = 8000 * (1 + 0.26)^t
Solving for t using a calculator or computer program, we find that:
t ≈ 5.02
Therefore, it will take approximately 5 years for the rabbit population to reach 25,000.