Question 294285: The half-life of Uranium-238 is approximately 4,560 million years. If 40% of the Uranium-238 in a rock has decayed, then how old is the rock?
Answer by nerdybill(7384)   (Show Source):
You can put this solution on YOUR website! The half-life of Uranium-238 is approximately 4,560 million years. If 40% of the Uranium-238 in a rock has decayed, then how old is the rock?
.
Exponential growth formula:
y(t) = a*e^(kt)
where
a is the initial value
y(t) is value at time t
t is time
k is the constant rate of growth or decay
.
Given that we know the half-life we can calculate k:
Let a = original amount
then
a/2 = a*e^(k*4560)
Dividing both sides by 'a':
1/2 = e^(k*4560)
ln(1/2) = 4560k
ln(1/2)/4560 = k
-1.52001*10^-4 = k
.
Now, we can answer:
If 40% of the Uranium-238 in a rock has decayed, then how old is the rock?
Let a = original amount
then
.40a = a*e^(-1.52001*10^-4 * t)
Dividing both sides by 'a':
.40 = e^(-1.52001*10^-4 * t)
ln(.40) = -1.52001*10^-4 * t
ln(.40)/-1.52001*10^-4 = t
6028 million years = t
|
|
|
