Question

I know you have to use the half life formula but I don’t know how to use it could someone show how to find the solution step by step? Thank you

Answer 1

`A = Pe ^(-0.03108 * t)`

Explanation:

Note: these are typically two part questions...

you have the model and have to FIRST find a constant value "k"

once you have the "k" value you plug that into the model to finish the problem

`A = Pe ^(-kt)` is a typical version of the continuous decay...

e is "e 2.717" not a variable "e"

so... step 1.. fink k

you are told that the 1/2 life is 22.3 years...

so lets assume that we started with 2 units of lead, and waited for it to decrease to 1 (1 is 1/2 of 2)

you would have

1 = 2
`e^(k * 22.3)`

.5 =
`e^(k * 22.3)`

ln(.5) = 22.3k ln(e)

ln(e) = 1

ln(.5) = 22.3k

ln(.5) = 22.3k ln(e)

`(ln(.5) )/(22.3) = k`

`(\ln \left(0.5\right))/(22.3)=-0.03108` = k