A local snail population grows according to the function g(x) = 200(1.03)2x. Demonstrate the steps to convert g(x) into an equivalent function with only x as the exponent. Then, explain to Iris how the key features of this local snail population compares to the key features of the invasive population.

I did the first part, but I need help doing the second part.

Question

A local snail population grows according to the function g(x) = 200(1.03)2x. Demonstrate the steps to convert g(x) into an equivalent function with only x as the exponent. Then, explain to Iris how the key features of this local snail population compares to the key features of the invasive population.
 
I did the first part, but I need help doing the second part.

thomas5267 · Answer

Note:
$$
a^{bc}=\left(a^b\right)^c\
\text{For example:}\
2^{3\times2}=64\
\left(2^3\right)^2=8^2=64
$$

jozelynw · Answer

@thomas5267  what exponential property is that?

jozelynw · Answer

so like this g=200(1.03^2)^x

jozelynw · Answer

@thomas5267

thomas5267 · Answer

I am unaware of a name for that property, even after a Google search.  It just works.  To prove this property, you first have to define exponentiation, which is a non-trivial task.  I would recommend you to just use it and not worry about it.

jozelynw · Answer

@nickmeneses1997 and @MathMan77  @mathmate

anonymous · Answer

I am also not sure of the name but I know that is correct, sorry

jozelynw · Answer

@MathMan77 what about the second part.

jozelynw · Answer

@emma.monsterr