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 11 months 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.
 11 months 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
 11 months ago
Best ResponseYou've already chosen the best response.0The halflife formula is: dw:1389736938636:dw

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

Emily778
 11 months ago
Best ResponseYou've already chosen the best response.0how do I do the rest?

coolsday
 11 months 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
 11 months ago
Best ResponseYou've already chosen the best response.0wouldn't the answer be 146.85?

Emily778
 11 months ago
Best ResponseYou've already chosen the best response.0by plugging those in?

dape
 11 months 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
 11 months 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.

Emily778
 11 months ago
Best ResponseYou've already chosen the best response.0So that's the answer?

coolsday
 11 months 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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