# algebra 4

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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 -

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 -

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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