A radioactive isotope has a half life of 700 years. If there is currently 6 mg of the isotope then how much was there 350
years ago?
A) 7.74 mg
B) 8.49 mg
C) 9.24 mg
D) 9.99 mg
E) 10.74 mg

Question

A radioactive isotope has a half life of 700 years. If there is currently 6 mg of the isotope then how much was there 350
years ago?
A) 7.74 mg 
B) 8.49 mg 
C) 9.24 mg 
D) 9.99 mg 
E) 10.74 mg

yuki · Answer

hey, still having trouble with decays ?

yuki · Answer

half life problems are the same as the other exponential decay problems , it only focuses on how long it takes so that the size of the object is half.

yuki · Answer

so instead of just

$$N_t = N_0(R)^{t}$$

you can now use

$$N_t = N_0(1/2)^{t/h}$$

yuki · Answer

where h is the half life

yuki · Answer

so in your problem, the initial amount is what we are looking for
and N_t is 6 mg while h =700. 

$$6 = N_0(1/2)^{350/700}$$

t = 350 because 350 years later, the amount is 6mg.
in other words, now it is 6mg and we want to know how much
it was 350 years ago

yuki · Answer

so

N_0 is approximately 8.49

yuki · Answer

I need to go, so just remember the eqn I taught you, ok?

good luck :)