Answer
Initial Quantity= 2.16 grams
Amount after 10,000 years= 1.621 grams
Work Step by Step
Start with the Exponential function
$y= Ce^{kt} $
Solve for k by using the half life of 24,100 years
$.5= e^{24,100k} $
$ - \ln{2} = 24100k$
$k= -\frac{\ln 2}{24100}$
now we get the equation
$y= Ce^{-\frac{\ln 2}{24100}t} $
Plug in the amount after 1000 years to find the initial amount C
$2.1= Ce^{-\frac{\ln 2}{24100} 1000} $
$ 2.1= 0.9716 C$
$C= 2.1613$ grams
Using C and k, find the amount after 10,000 years
$y= 2.1613e^{-\frac{\ln 2}{24100}10,000} $
$y= 1.621$ grams
