Exponential and logarithmic functions.. PLZ HELP?

the half life of a certain radioactvie substance is 12 hours. There are 8 grams present initially.
Express the amount of substance remaining as a function of time t.

Answer:
P = A(1/2)^(t/12)
P = 8(1/2)^(t/12)
This is a simple differential equation problem.
dN/dt = -yN
1/N dN = -y dt
ln N = -yt + c
N(t)=e^(-yt+c)
N(t) = Ce^(-yt)
N(0) = 8 = Ce^(0)
C=8 (initial amount)
N(t)=8e^(-yt)
N(12)=4=8e^(-12t)
.5=e^(-12y)
y=.0577
N(t) = 8e^(-.0577t)

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