Question

The population f(x), in millions, of State A of a country after x years is represented by the function shown below: f(x) = (1.08)x The graph shows the population g(x), in millions, of State B of the country after x years: Graph of function g of x equals 2 multiplied by 1.08 to the power of x Which conclusion is correct about the population of State A and State B? The original population of State B was half of the original population of State A. The original population of State A was half of the original population of State B. The original population of State B was one-fourth of the original population of State A. The original population of State A was one-fourth of the original population of State B.

Answer 1

The answer is C, or "The original population of State A was half of the original population of State B."

Answer 2

-- State-A . . . Population = 1 · (1.08)ˣ

-- State-B . . . Population = 2 · (1.08)ˣ

' x ' = number of years after the original population
At the beginning, x=0.
Any quantity raised to the zero power = 1.
At the beginning, when x=0, the original populations were
State-A = 1 · 1 = 1
State-B = 2 · 1 = 2

The original population of State A was half of
the original population of State B.