Simplifying Exponents

I don't like the use of the word "simplify". The variable "t" evaluates to a real number.

This looks like a homework problem (and I don't do homework), but I will help get started. Can you translate this into an expression with a logarithm?

Hint: it will be in the form of A = log(B)C

If you get to this point, and need it, I will give you another hint.

We have not studied logarithms yet. This came from a problem about exponential decay.

There is nothing further you can do with this expression that does not involve logarithms.

Logarithms were invented for exactly this, to find exponents.

Here is the wikipedia page which is pretty helpful, the first paragraph should give you what you need if you want to try it. If you have a decent calculator it will have a "logxy" button that will give you the answer.

Wikipedia:logarithms

I suppose I can just estimate based off of a graph. Thanks for your help.

Yes. If you can make a graph of y = .39^x, that is a fine way to get a reasonable answer (and is educational too).

You welcome.