Final answer:
The population of butterflies after 7 years is approximately 2805.1.
Step-by-step explanation:
The function f(x) = 2,000(1.05)^x represents the population of butterflies after x years. To find the population in 7 years, substitute x = 7 into the function:
f(7) = 2,000(1.05)^7
Using a calculator, we can evaluate this to:
f(7) ≈ 2,000(1.402551) ≈ 2805.1
Therefore, the population of butterflies after 7 years is approximately 2805.1.