If 90% of the initial amount of a radioactive element remains after one day, what is the half life of the element?
Using exponential decay
Using exponential decay
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a = pe^(-rt)
Assume 100 grams of the substance exists at t=0.
Solve the above equation for 90 grams as follows:
90 = 100e^(-r*1) = 100e^(-r)
0.9 = e^(-r)
ln(0.9) = -r
r = -ln(0.9) = 0.1054
a = pe^(-0.1054t)
Now solve the equation for t for 50 grams (half-life):
50 = 100e^(-0.1054t)
0.5 = e^(-0.1054t)
ln(0.5) = -0.1054t
t = ln(0.5) / (-0.1054) = 6.5763 days
Assume 100 grams of the substance exists at t=0.
Solve the above equation for 90 grams as follows:
90 = 100e^(-r*1) = 100e^(-r)
0.9 = e^(-r)
ln(0.9) = -r
r = -ln(0.9) = 0.1054
a = pe^(-0.1054t)
Now solve the equation for t for 50 grams (half-life):
50 = 100e^(-0.1054t)
0.5 = e^(-0.1054t)
ln(0.5) = -0.1054t
t = ln(0.5) / (-0.1054) = 6.5763 days