Question

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 the equation: P=100(0.00007)t.How much plutonium is present after 20,000 years?

Answer 1

Answer:

That equation is not typed correctly.  Radioactivity decreases by what is known as exponential decay.

Pu 239 has a half-life of  24,100 years.  

We need to calculate lambda which is natural log (2) / half-life

lambda = .693147 / 24,100 = 2.876 x 10^-5

Amount remaining = beginning amount • e ^ ( -λ • time )

Amount remaining = 100 * 2.718281828^(-2.876 x 10^-5 * 20,000)

Amount remaining = 100 * 2.718281828^-.5752

Amount remaining = 100 * 0.5625923391

Amount remaining after 20,000 years = 56.25923391 grams

Source: https://www.1728.org/halflif2.htm

Step-by-step explanation: