Half Life of the element Michaelonium is 4 hours

Question

The half life of the element Michaelonium is 4 hours Find a constant a so that the function e^ax gives the fraction of Michaelonium present after x hours.

Answer 1

P left = Po(1/2)^(x/4), in 4 hours 1/2 is left = Po/2 = half what you started with

in 8 hours, Po/4 left, in 12 hours Po/8 left

but you want in terms of e^ax

P = Poe^ax

1/2 = e^ax = e^4a

ln.5 = 4a

a = (ln.5)/4= about -.1732

P = Poe^((ln.5)/4)

= about Poe^-.1732