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Emily778
 2 years ago
The halflife of a radioactive substance is the time it takes for half of the material to decay. Phosphorus32 is used to study a plant's use of fertilizer. It has a halflife of 14.3 days. Write the exponential decay function for a 50mg sample. Find the amount of phosphorus32 remaining after 84 days.
Emily778
 2 years ago
The halflife of a radioactive substance is the time it takes for half of the material to decay. Phosphorus32 is used to study a plant's use of fertilizer. It has a halflife of 14.3 days. Write the exponential decay function for a 50mg sample. Find the amount of phosphorus32 remaining after 84 days.

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coolsday
 2 years ago
Best ResponseYou've already chosen the best response.0The halflife formula is: dw:1389736938636:dw

coolsday
 2 years ago
Best ResponseYou've already chosen the best response.0A is the final amount , Ao is the initial amount, h is the halflife of the substance, and t is the time

coolsday
 2 years ago
Best ResponseYou've already chosen the best response.0just plug the variables into the formula to solve for A.

coolsday
 2 years ago
Best ResponseYou've already chosen the best response.0Ao is 50 mg, h is 14.3, t is 84 plug it into the formula and solve for A

Emily778
 2 years ago
Best ResponseYou've already chosen the best response.0wouldn't the answer be 146.85?

dape
 2 years ago
Best ResponseYou've already chosen the best response.1So the halflife 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.

dape
 2 years ago
Best ResponseYou've already chosen the best response.1Oh, 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.

coolsday
 2 years ago
Best ResponseYou've already chosen the best response.00.85 mg will remain after 84 days if you use the formula.
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