# Calculus-Modeling Equations

An unknown radioactive element decays into non-radioactive substances. In 420 days the radioactivity of a sample decreases by 39 percent.

1.What is the half-life of the element?

2.How long will it take for a sample of 100 mg to decay to 46 mg?

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1. A(t)= Ao* (1/2)^(t/h)
where h is the half life.
A/Ao = 1-0.39 = 0.61
0.61 = (1/2)^(420/h)
log 0.61 = (420/h) log (1/2)
420/h = 0.71312
h = 589 days

When 100 mg becomes 46 mg of radioactive material, A/Ao = 0.46
0.46 = (1/2)^(t/589)
t/589 = log(0.46)/log(0.50)= 1.1203
t = 660 days

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