Question

The population of an ant colony can be modeled by the function f(x) = 100 (2)*. Which of the following would be an appropriate representation of the domain?

A. (-∞, ∞)
8. [2, 100]
O
C. [2,∞)
D. [0, ∞)

Answer 1

The domain of the function f(x) = 100 (2)^x, representing an ant colony population, would be [0, ∞), which allows for all stages of growth from the initial time, marked by x = 0, onwards. The correct answer is option D.

Step-by-step explanation:

The population of an ant colony can be modeled by the function f(x) = 100 (2)*. It seems there might be a typo in the function provided, as the mathematical expression is incomplete.

However, assuming the intention was f(x) = 100 (2)^x, the function describes exponential growth and the domain would be all non-negative real numbers, because time or growth phases (usually represented by 'x' in such functions) cannot be negative in this context. One cannot go back in time or have negative stages of growth of a colony.

Therefore, the appropriate representation of the domain for f(x) = 100 (2)^x would be [0, ∞) since the population can be defined from time zero to infinity. The answer is Option D.