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shepuryov [24]
3 years ago
9

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

Mathematics
1 answer:
n200080 [17]3 years ago
7 0

Answer:

A = Pe ^{-0.03108 * t}

Step-by-step 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 = 2e^{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)

\frac{ln(.5) }{22.3} = k

\frac{\ln \left(0.5\right)}{22.3}=-0.03108 = k

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