The population f(x), in millions, of State A of a country after x years is represented by the function shown below:

f(x) = 4(1.08)x

The graph shows the population g(x), in millions, of State B of the country after x years:

graph of exponential function g of x that curves up from left to right and goes through points 0 comma 2 and 9 comma 4

Which conclusion is correct about the populations of State A and State B?

Question

notimportant0016 notimportant0016

11-07-2022
Mathematics

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The population f(x), in millions, of State A of a country after x years is represented by the function shown below:

f(x) = 4(1.08)x

The graph shows the population g(x), in millions, of State B of the country after x years:

graph of exponential function g of x that curves up from left to right and goes through points 0 comma 2 and 9 comma 4

Which conclusion is correct about the populations of State A and State B?

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ogorwyne ogorwyne · Answer 1 · 2022-07-12T19:26:19+02:00

Option 1 is correct. The correct solution about these functions is that The original population of State A was double of the original population of State B.

How to solve for the solution

The function in the question is given as

For A:

[tex]F(x) = 4*(1.08)^x[/tex]

For B

[tex]g(x) = 2*(1.08)^x[/tex]

The exponential growth equation that is used to solve this is

[tex]h(x) = A(r)^x[/tex]

such that A is the initial and r is the rate of growth.

f(x) and g(x) are at the same rate but the exponential function is known to grow faster.

Hence the correct option is The original population of State A was double of the original population of State B.

Complete question:

Which conclusion is correct about the population of State A and State B? 1. The original population of State A was double of the original population of State B.

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

3. The original population of State B was one-fourth of the original population of State A.

4. The original population of State A was one-fourth of the original population of State B.