Hello, alderon!

The "decay" formula is: .A certain radioactive material has a half-life of 38 hours.

Find how long it takes for 90% of the radioactivity to be dissipated?

. . where = initial amount, = final amount,

. . = time, and is a constant to be determined.

We are told that when

So we have: .

Multiply by

Hence, we have: .

The problem asks: .When is ?

We have: .

Multiply by

Therefore: .