a sample of 32 grams of an unknown substance has a half -life of 12 years.
1. write an equation to the determine the amount of a substance,s,left after t years.
2. approximately how long will it take for 0.1 grams f the substance to remain (to the nearest year)
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Step-by-step explanation:
We need to apply the exponential decay function.
The exponential decay function is given as:
The remaining substance A(t) at time t is given by :
A(t) = A(0)e^-kt
The half life t is given by :
-ln 2/k = t
Since we have the half life we can get k.
16 = - ln2 / k
k = - ln 2/ 16
k = - 0.04332
A(0) = the initial amount = 32 grams
1) A(t) = 32e^-0.04332t
2) A(t) = 0.1 gram
0.1 = 32e^-0.04332t
0.1/32 = e^-0.04332t
0.003125 = e^-0.04332t
Taking ln on both sides we have :
ln 0.003125 = - 0.04332t
t = ln 0.003125/-0.04332
= 133.16 years.
To the nearest year is 133 years.
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