SOLUTION: 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

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.
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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
where:
Y = amt after t time (10 mg)
Yo = initial amt (20 mg)
k = half-life of the substance
t = time of decay (200)
:

ln of e is 1, therefore

200k = -.693147
k =
k = -.0034657
:
:
Check this on your calc: 20*e^(-.0034657*200) = 10.000
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