## Emily778 Group Title The half-life of a radioactive substance is the time it takes for half of the material to decay. Phosphorus-32 is used to study a plant's use of fertilizer. It has a half-life of 14.3 days. Write the exponential decay function for a 50-mg sample. Find the amount of phosphorus-32 remaining after 84 days. 6 months ago 6 months ago

1. coolsday Group Title

The half-life formula is: |dw:1389736938636:dw|

2. coolsday Group Title

A is the final amount , Ao is the initial amount, h is the half-life of the substance, and t is the time

3. coolsday Group Title

just plug the variables into the formula to solve for A.

4. Emily778 Group Title

how do I do the rest?

5. coolsday Group Title

Ao is 50 mg, h is 14.3, t is 84 plug it into the formula and solve for A

6. Emily778 Group Title

7. Emily778 Group Title

@coolsday

8. Emily778 Group Title

by plugging those in?

9. dape Group Title

So the half-life formula can also be written as $$2^{-\lambda t}$$, where $$\lambda$$ is the 'decay constant', or just $$1/h$$, where h is half life. So the exponent is $$84/14.3\approx5.874$$, which says that the sample will have time to halve in size about 5.9 times in the 84 days (this is an easy way to remember the formula). Putting this in, we have that $$2^{-84/14.3}\approx1.7\%$$. So about 1.7% of the sample will remain. Starting with 50 mg this means that about $$50\times1.7\%=0.85$$ mg of the sample will remain.

10. dape Group Title

Oh, and the 'exponential decay function' we just get by putting all this together, so $P(t)=50\times2^{-t/14.3}$ Where t is time in days.

11. Emily778 Group Title

12. Emily778 Group Title

@dape

13. Emily778 Group Title

hellloooo?

14. coolsday Group Title

0.85 mg will remain after 84 days if you use the formula.