SOLUTION: A certain reproductive element decays according to A(t) = A(0,e^-0.032t). Where t is years. How long would it take to go from 800 grams to 85 grams? (nearest year)

Question 185318: A certain reproductive element decays according to A(t) = A(0,e^-0.032t). Where t is years. How long would it take to go from 800 grams to 85 grams? (nearest year)
Found 2 solutions by ankor@dixie-net.com, ZeratuelX:
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
A certain reproductive element decays according to A(t) = A(0,e^-0.032t).
Where t is years. How long would it take to go from 800 grams to 85 grams?
(nearest year)
;
I think the formula you mean is: A(t) = A(e^-0.032t)
A = 800
A(t) = 85
Find t:
:
800*e^-.032t = 85
:
Divide both sides by 800:
=
:
The natural log of both sides:
-.032t*ln(e) = ln(.01625)
:
Natural log of e = 1, therefore:
-.032t = -2.24196
:
t =
t = 70 yrs f0r 800 grms to decay to 85 grms
;
:
Check on a calc: enter: 800*e^(-.032*70) = 85.17 ~ 85

Answer by ZeratuelX(5) (Show Source): You can put this solution on YOUR website!
In this question we will have to use the Continuously Compounded Interest Formula which is represented by the equation where A is the resulting number, P is the original number, r is the rate, and t is the time.
-----
In this question we have an original value of 800 grams, and an ending value of 85 grams so we can set up the equation like this:

Since we are trying to find how long it will take, we are trying to solve for t (time). To get a variable out of the exponent we will have to take the logarithm of both sides after the problem is simplified.
(Divide both sides by 800)
(Take the natural log of both sides, log base e)
(Use the logarithm power property to take the exponent out)
(Divide both sides by -0.032)
(Solve the natural log with a calculator)
(Round to the nearest number of years)
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