The half life of Pb-210 is 22 years. A decayed animal shows 48% of the original Pb-210 remains; how long has the animal been deceased to the nearest tenth of a year?

0.01 years
23.3 years
22.29 years
0.04 years

Question

The half life of Pb-210 is 22 years. A decayed animal shows 48% of the original Pb-210 remains; how long has the animal been deceased to the nearest tenth of a year?
 	
	0.01 years
	23.3 years
	22.29 years
	0.04 years

asnaseer · Answer

Do you know how to represent half-life as an equation?

hulkart · Answer

no

asnaseer · Answer

Does this equation look familiar to you at all?$$A=A_0\times\left(\frac{1}{2}\right)^{\frac{t}{h}}$$

hulkart · Answer

so can you plug it in?

asnaseer · Answer

You need to first understand this equation - have you seen anything like it before?

hulkart · Answer

no

asnaseer · Answer

OK - let me try to explain it to you...

asnaseer · Answer

When we have some substance that decays according to the half life rule then we have:
1. $A_0$ represents the initial amount of a substance
2. $h$ represents the half life of the substance (in your question we have $h=22$ years) 
3. $t$ represents the amount of time that has elapsed (in your question this would be measured in years)
4. $A$ represents the amount of substance left after time $t$ has elapsed

Does this make sense to you?

hulkart · Answer

kinda...

asnaseer · Answer

In your question the substance being talked about is Pb-220 (a form of lead). So $A$ represents the amount of this lead left after $t$ years have elapsed. If we take your question where we have $h=22$ we get:$$A=A_0\times\left(\frac{1}{2}\right)^{\frac{t}{22}}$$Following so far?

hulkart · Answer

don't worry I can continue on my own

asnaseer · Answer

great - why don't you let me know when you have an answer and I will check it for you. Just ping me when you are ready.

hulkart · Answer

ok...