Function: y= 1200(.891)^t ( I think the .891 you might check rest is okay) A dif

Question

Function: y= 1200(.891)^t ( I think the .891 you might check rest is okay)
A diffferent radioactive substance loses half its mass over a 6 yr period of time(or half life is 6 yrs). A 1200 gram sample will decay into a 600 gram sample after 6yrs.
1. Determine the approx. rate at which the sibstance decays per yer. Then writethe equation for its mass (y) over time (t) in years.

2. With your equation, find y(12) and y(18). Do these values make sense.
3. For what interval of time will the amount of the substance be greater than 400 grams/ Solve by table.
These given:
0= 1200.
1= 1069.1
2= 952.4
3= 8485
4=756.0
5= 673.5
6=600.

Explanation / Answer

1. If the substance loses half of his mass over a six year period, it will lose 1/12 of its mass each year. Assuming that the equation is of the form: y=Ne^(kt) If we plug in 6 for t, y will be N/2. This will allow us to solve for k 1/2=e^(6k) ln(1/2)=-6k k=ln(1/2)/6 So y = 1200e^(ln(1/2)t/6) 2) y(12) = 300 y(18) = 150 These answers because 12 is 2 half-lives and 300 is 1/4 of 1200 Similarly 18 is 3 half-lives and 150 is 1/8 of 1200

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