Final answer:
The population in two years is expected to be around 22,974, applying the exponential growth formula P = P0(2)^(t/D) where P0 is the initial population, t is the time in months, and D is the doubling time.
Step-by-step explanation:
If the population doubled in size over 20 months and the current population is 10,000, to find what the population will be 2 years from now, we need to first understand the rate of growth. The population doubling in 20 months suggests an exponential growth pattern.
We use the formula for exponential growth: P = P0(2)^(t/D) , where P is the final population, P0 is the initial population, t is the time in months, and D is the doubling time in months.
In this case, D is 20 months (the given doubling time), and we want to calculate the population P 2 years (or 24 months) from now. Substituting the values, we get: P = 10,000(2)^(24/20). When simplified, P = 10,000(2)^(1.2). Calculating the value gives us P ≈ 10,000 * 2.2974, which equals approximately 22,974. Hence, the population in two years is expected to be around 22,974.