Question

Please help me answer this. My professor taught us this but with the formula on the right.

Answer 1

First lets rearrange the formula to solve for half-life.
The half-life is the time it takes for half of the element to decay.

`e^(rt) = (1)/(2) \\ t = (ln ((1)/(2)))/(r)`

So now we need to find "r" which is the rate of decay.
If we rearrange formula to solve for r:

`P e^(rt) = A \\ \\ r = (ln ((A)/(P)))/(t)`

Substituting this into equation for half-life, you get:

`T = (( ln (1/2))/(ln (A/P)) ) t = ( ln(1/2))/(ln (200/500)) *(48) = 36.31`