a certain radioactive material has a half-life of 38 hours.find how long it takes for 90% of the radioactivity to be dissipated?
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: .