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the mass of a radioactive substance follows a continuous exponential decay model, with a decay rate parameter of per day. a sample of this radioactive substance was taken six days ago. if the sample has a mass of today, find the initial mass of the sample. round your answer to two decimal places.



Answer :

varshamittal029

Either this is exponential decay at 8% loss per day or it is not. You need to know or decide which it is.

Start with A=p%2Ae%5E%28-kt%29 if this is the kind of model wanted. The variables are

A, amount after passage of time t

p, initial amount when t=0

t, time passage in days

e, base for the Natural Logarithm

k, a constant

First, find the value for k using your 8% loss per day.

For t=1, p=1, A=0.8.

ln%28A%29=ln%28p%29%2Bln%28e%5E%28-kt%29%29

ln%28A%29-ln%28p%29=-kt%2A1

kt=ln%28p%29-ln%28A%29

highlight_green%28k=%281%2Ft%29%28ln%28p%2FA%29%29%29

Substitute the known or given values and evaluate k.

k=%281%2F1%29ln%281%2F0.8%29

k=ln%281.25%29

highlight28k=0.223 29-

The model for your example is A=p%2Ae%5E%28-0.223t%29, or using your given initial quantity of material, highlight%28A=2.01e5E28-0.223t2929

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