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

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

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.

To calculate the amount of plutonium present after 20,000 years, we can substitute t = 20,000 into the exponential decay model equation:

p = 100(0.99997)^t

p = 100(0.99997)^20000

Using a calculator or a computer program, we can evaluate this expression:

p ≈ 100(0.99997)^20000 ≈ 78.759942 grams

Therefore, approximately 78.76 grams of plutonium would be present after 20,000 years.

To find how much plutonium is present after 20,000 years, you can use the given exponential decay model equation:

p = 100(0.99997)^t

Plug in the value of t as 20,000 in the equation and calculate:

p = 100(0.99997)^20000

Now, let's solve it step by step:

Step 1: Calculate 0.99997 raised to the power of 20,000:

(0.99997)^20000 ≈ 0.6702

Step 2: Multiply the result by 100:

p ≈ 100 * 0.6702 ≈ 67.02

Therefore, after 20,000 years, there will be approximately 67.02 grams of plutonium present in the container.