Question

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Answer 1

Hi!
There is actually two ways to solve these half-life problems. One is using a formula, while the other is intuitive. I will set it up with the formula and show you how to answer it.

1. Using the formula Amount=OriginalAmount(1/2)^(time/half-life) we can plug in what we have to deduce the answer:
5g=40g(1/2)^(time/1.25billion years)
Note: we found 5g since there was 12.5% of 40g still remaining, so .125*40g
Dividing by 40 would give .125, or 1/8 on the left side.
We know 1/8=(1/2)^3, so going back to the equation, the time must be 3 times the half-life, hence the answer 3.75 billion years.

2. Set it up the same way, but this time you might need a calculator for 21.88g/175g. You will turn out to get 1/8 again. Now, you know the time needs to be 3x the half-life, giving us an answer of .75 years.

Hope I helped!

Answer 2

Thank you so much. I understand how to do it now