Question

The amount of time T (in years) it will take for a population of a certain species to grow from 3500 to a can be modeled by the function Y(a)=log _(5) (a/3500)^1/0.03. Which function is equivalent?

Answer 1

Option C is correct

Explanation:

Here, we want to find which of the equations in the option is same as that in the question

The rule to use is that;

Loga B^y

= ylogaB

And also:

loga(X/Y) = logaX-logaY

Now, we start by applying these equations;

T(a) = log5 (a/3500)^1/0.03

T(a) = 1/0.03log5(a/3500)

T(a) = 1/0.03log5a - 1/0.03log53500

This makes the third option correct