Question 817354
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Hi,
The Half-life of carbon-14 is 5700 years.
{{{Q(t) = Q[0]e^(-kt)}}}
.5  = {{{ e^(-5700k )}}} ,  {{{ln (.5)/ -5700}}} = k,  k = .00012&#61614; 
 A sample of carbon 14 originally contained 75 grams. 
 A) Based off this information please create an equation {{{Q(t) = 75e^(-.00012t)}}}
 B) What is a reasonable domain and range for your model in the context of this problem? Domain all real numbers t &#8805; 0, 
Range 0 > Q(t) &#8804; 75
 C) Use your model to predict the amount of carbon 14 left in the sample after 2000 years.
{{{Q(2000) = 75e^(-.00012*2000)}}}
 D) How ling will it take for the sample to contain only 10 grams of carbon 14
 10/75 = e^(.00012t), {{{t = ln (10/75)/(-.00012) }}}  
 E) How long will it take for 80% of the carbon 14 in the sample to decay?     
.80= e^(-.00012t), {{{t = ln (.8)/(-.00012) }}}