SOLUTION: The​ half-life of a radioactive substance is 36.1 years. a. Find the exponential decay model for this substance. A(t)=A0e^__t (Round to the nearest tenth) b. How long will it

Algebra ->  Equations -> SOLUTION: The​ half-life of a radioactive substance is 36.1 years. a. Find the exponential decay model for this substance. A(t)=A0e^__t (Round to the nearest tenth) b. How long will it       Log On


   

Question 1193732: The​ half-life of a radioactive substance is 36.1 years.
a. Find the exponential decay model for this substance.
A(t)=A0e^__t (Round to the nearest tenth)
b. How long will it take a sample of 400 grams to decay to 300 ​grams?
Approximately ___ years (Round to the nearest hundredth)
c. How much of the sample of 400 grams will remain after 20 ​years?
About ___ Grams (Round to the nearest integer)
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Problem description indicates the model form must be A%28t%29=A%5Bo%5De%5E%28kt%29 form.
Use the half life fact to find the value for k.

1%2Ae%5E%28kt%29=1%2F2
e%5E%28kt%29=1%2F2
ln%28e%5E%28kt%29%29=ln%281%2F2%29
kt=-ln%282%29
k=-ln%282%29%2Ft
highlight_green%28k=-ln%282%29%2F36.1%29
highlight%28k=-0.01920%29

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highlight%28A%28t%29=A%5Bo%5De%5E%28-0.01920t%29%29