MHR • Advanced Functions 12 Solutions 660
MHR • Advanced Functions 12 Solutions 660
MHR • Advanced Functions 12 Solutions 660
Create successful ePaper yourself
Turn your PDF publications into a flip-book with our unique Google optimized e-Paper software.
e) How old is bone that contains 10% of its original carbon-14?<br />
Solution:<br />
0.1 = 0.999!<strong>12</strong>2(0.999!875) t<br />
0.1<br />
log = log 0.999!875t<br />
0.999!<strong>12</strong>2<br />
0.1<br />
log = t log 0.999!875<br />
0.999!<strong>12</strong>2<br />
0.1<br />
log<br />
t =<br />
0.999!<strong>12</strong>2<br />
log 0.999!875<br />
t &= 18!4<strong>12</strong>.5<br />
The bone is about 5545 years old.<br />
Using the formula from the exponential regression, determine the half-life of carbon-14.<br />
Solution:<br />
t<br />
! 1$<br />
h<br />
"<br />
#<br />
2%<br />
& = 0.999!875<br />
t<br />
t<br />
!<br />
log 1 $ h<br />
"<br />
#<br />
2%<br />
& = log 0.999!875<br />
t<br />
t<br />
h log ! 1 $<br />
"<br />
#<br />
2%<br />
& = t log 0.999!875<br />
!<br />
t log 1 $<br />
"<br />
#<br />
2%<br />
&<br />
h =<br />
t log 0.999!875<br />
!<br />
log 1 $<br />
"<br />
#<br />
2%<br />
&<br />
h =<br />
log 0.999!875<br />
h &= 5545<br />
The half-life is about 5545 years.<br />
<strong>MHR</strong> <strong>•</strong> <strong>Advanced</strong> <strong>Functions</strong> <strong>12</strong> <strong>Solutions</strong> 729
Change language