Decaying question

Question

There is a radioactive substance we have stumbled upon and we start doing some tests with it. We realize it is decaying. It is useful to us as long as we have at least 25% of the initial amount we obtained. If the half life of this substance is 37 years, how long with the substance be useful to us?

Answer 1

A = a₀(0.5)^t/h, where a₀ = starting amount, h = half life, t = time

 

0.25a₀ = a₀(0.5)^t/37

0.25 = (0.5)^t/37

ln 0.25 = (t/37) ln 0.5

-1.38629436 ≈ (t/37) (-0.693147181)

2= t/37

74 = t

 

The sample is good for 74 years.

 

Or, without all the Algebra.

 

After 37 years 50% is left. After another 37 years 25% is left. So the sample is good for 74 years.

Sometimes understanding what is going on in the problem and thinking is faster than Algebra!