Decay problems will usually follow this equation format:
N(t) = N0e^(-rt)
Where N(t) is the amount of material after time t, N0 is the starting amount, t is time, and r is a rate constant.
They tell us that the half-life of iodine is 8 days. So after 8 days, N(8) = N0/2. We can use this information to find the rate constant.
N0/2 = N0e^(-r(8 days))
0.5 = e^(-r(8 days))
ln(0.5) = -r*8 days
-ln(0.5)/8days = r
r = 0.087 * 1/day
Now that we have the rate constant, we can answer the next question: how much of the iodine is in the patient's body after 20 days?
N(20) = 6g*e(-0.087 * 1/day * 20 days)
N(20) = 6g*e(-1.74)
N(20) = 1.05g
One last question! How long will it take before there are 2g iodine left in the patient's body?
2g = 6g*e(-0.087 * 1/day * t)
1/3 = e(-0.087 * 1/day *t)
ln(1/3) = -0.087 * 1/day *t
ln(1/3)*day/-0.087 = t
t = 12.6 days
