Question

The half-life of plutonium-244 is 80,000,000 years. Express the amount of plutonium-244 remaining as a function of time, measured in years with starting quantity A0.

Answer 1

The exponential function for the amount of plutonium-244 remaining as a function of time is given by:

$A(t) = A(0)e^{-0.00000000866t}$

What is an exponential function?

A decaying exponential function for the amount of a substance is modeled by:

$A(t) = A(0)e^{-kt}$

In which:

• A(0) is the initial value.

• k is the decay rate, as a decimal.

The half-life of plutonium-244 is 80,000,000 years, hence $A(80000000) = 0.5A(0)$, which is used to find k.

$A(t) = A(0)e^{-kt}$

$0.5A(0) = A(0)e^{-80000000k}$

$e^{-80000000k} = 0.5$

$\ln{e^{-80000000k}} = \ln{0.5}$

$-80000000k = \ln{0.5}$

$k = -\frac{\ln{0.5}}{80000000}$

$k = 0.00000000866$

Hence, the function is:

$A(t) = A(0)e^{-0.00000000866t}$

You can learn more about exponential functions at https://brainly.com/question/25958656