SOLUTION: if the half life is 18 years and the initial amount is 139, how much remains after 5 years...: calculus

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Question 403709: if the half life is 18 years and the initial amount is 139, how much remains after 5 years...: calculus
Answer by richard1234(7193) About Me  (Show Source):
You can put this solution on YOUR website!
The formula for exponential decay is A+=+A%5B0%5D%2Ae%5Ekt where A%5B0%5D+=+139, k is some constant, and t is time. Also, we have

69.5+=+139%2Ae%5E%2818k%29 given the half-life

1%2F2+=+e%5E%2818k%29

18k+=+ln%281%2F2%29+=+ln+%281%29+-+ln+%282%29+=+-ln+%282%29

k+=+%28-ln+%282%29%29%2F18

Now, substitute into your original equation for exponential decay and replace t = 5 years to solve.