SOLUTION: 8. Radioactive materials like uranium follow the law of uninhibited decay, which is an Exponential Model. This decay causes radiation. All radioactive substances have a specific ha

Question 825694: 8. Radioactive materials like uranium follow the law of uninhibited decay, which is an Exponential Model. This decay causes radiation. All radioactive substances have a specific half-life, which is the time required for half of the radioactive substance to decay. Uninhibited Radioactive Decay is given by the formula:

The half-life of thorium-229 is 7,340 years. How long will it take for a sample of this substance to decay to 20% of its original amount?

Answer by josgarithmetic(39617) (Show Source): You can put this solution on YOUR website!
The exponential decay model is based on ; some people might prefer a , but however the choice, consistency is needed.

A = amount at time t
I = initial amount, for t=0
k = a constant
t = time in years

First, find k.

'
The given halflife is for t=7340 years, and for which ;

'
Not sure if this will render properly but the model is:

Your specific question will use A=0.20, and I=1. You would then solve the model equation for t.
Recall from, "First, find k", a slight change in step gives: ; just substitute the values known.
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