Thread: Radioactive Logarithim

Hey guys, just found this forum after searching for days about this problem I've got. No where seems to have any relevant answers so I thought I might ask a forum for some help.
Basically I've got a Methods Assignment and I can't seem to work out if what I am doing is correct, any help would be great.
Here's the question:
The mass of a radioactive isotope is given by M=Mo(10)^-kt. It takes 200 years for the mass of the isotope to halve.
Find the initial mass (grams) in terms of M.
I assume Mo₁₀(10) is the initial mass and a logarithm, doesn't say though.

I've tried to solve this question like this:
M=Mo₁₀(10)^-kt
M=(-kt)Mo₁₀(10)
M/Mo₁₀(10)=-kt
Mo₁₀(10)/M=1/-kt
Mo₁₀(10)=-M/kt

Is this correct or have I made some kind of mistake, just doesn't seem right to me :/

If it takes 200 years for half of the isotope to decay, then we may state:

Well then, I was a little off.
But thank you so much, that makes more sense and helps me with the next part aswell