find how many half lives have passed
seems we are measuring in days
half life formula is as follows
[tex]A=P(\frac{1}{2})^\frac{t}{h}[/tex]
A=final amount
P=initial amount
t=time in a certain units (this time, it's days)
h=time of half life
so
we are given that P=1, A=0.6, t=3
find h
subsitute
[tex]0.6=1(\frac{1}{2})^\frac{3}{h}[/tex]
[tex]0.6=(\frac{1}{2})^\frac{3}{h}[/tex]
take ln of both sides
[tex]ln(0.6)=ln((\frac{1}{2})^\frac{3}{h})[/tex]
[tex]ln(0.6)=(\frac{3}{h})ln(\frac{1}{2})[/tex]
multiply both sides by h
[tex](h)ln(0.6)=3ln(\frac{1}{2})[/tex]
divide both sides by ln(0.6)
[tex]h=\frac{3ln(\frac{1}{2})}{ln(0.6)}[/tex]
use your calculator
h≈4.07075
so about 4 days is the half life
