Question 966341
An initial amount of a radioactive substance y0 is given, along with information about the amount remaining after a given time t in appropriate units.
 For an equation of the form y = y0ekt that models the situation, give the exact value of k in terms of natural logarithms: y0 = 20 mg; the half-life is 200 days.
:
The equation is:
Half remains after 200 days
{{{Y = Yo*e^(kt)}}} where:
Y = amt after t time (10 mg)
Yo = initial amt (20 mg)
k = half-life of the substance 
t = time of decay (200)
:
{{{20*e^(200k) = 10}}}
{{{e^(200k) = 10/20}}}
{{{e^(200k) = 1/2}}}
ln of e is 1, therefore
{{{200k = ln(1/2)}}}
200k = -.693147
k = {{{-.693147/200}}}
k = -.0034657
:
:
Check this on your calc: 20*e^(-.0034657*200) = 10.000