Posted by **derriel welch** on Wednesday, February 18, 2009 at 7:55pm.

write an exponential decay model that describes the situation.

one hundred grams of plutonium is stored in a container.the amount p (in grams) of plutonium present after t years can be modeled by this equation.

p=100(0.99997)t

hpw much plutonium is present after 20,000years

- algebra 4 -
**Damon**, Wednesday, February 18, 2009 at 8:08pm
you have a typo I think

The idea is that the amount lost per unit time is proportional to the amount present at each time

dp/dt = -k p

dp/p = -k dt

ln p = -kt

constant*p = e^(-kt)

find the constant when t = 0 so e^-kt = 1

p = 100 at t = 0

p = 100 e^-kt

so what you probably meant to type was that with k = .99997

so

p = 100e^-(.99997*20,000)

p = 0 on my calculator after 20,000 years

- algebra 4 -
**Reiny**, Wednesday, February 18, 2009 at 8:51pm
or the equation was given as

p = 100(.99997)^t

for t = 20000, my calculator gave me

p = 54.88 g

As Damon pointed out, your equation as it stands makes little sense.

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