posted by derriel welch on .
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.
hpw much plutonium is present after 20,000years
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
p = 100e^-(.99997*20,000)
p = 0 on my calculator after 20,000 years
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.