The half-life of carbon-14 is 5600 years. If charred logs from an old log cabin show only 71% of the carbon-14 expected in living matter, when did the cabin burn down?
Assume that the cabin burned soon after it was built from freshly cut logs?
Assume that the cabin burned soon after it was built from freshly cut logs?
1 Answer
The cabin burned down approximately
Explanation:
When dealing with a half life question, it is best to use the half-life formula, which is expressed as:
#color(blue)(|bar(ul(color(white)(a/a)y=a(b)^(t/h)color(white)(a/a)|)))# where:
#y=# final amount
#a=# inital amount
#b=# growth/decay
#t=# time elapsed
#h=# half-life
#a=1# is#100%# , expressed as a decimal#b=1/2# indicates half-life
#y=a(b)^(t/h)#
#0.71=1(1/2)^(t/5600)#
#log(0.71)=log((1/2)^(t/5600))#
#log(0.71)=(t/5600)log(1/2)#
#t/5600=(log(0.71))/(log(1/2))#
#t==(5600log(0.71))/(log(1/2))#
#color(green)(|bar(ul(color(white)(a/a)t~~2767.01color(white)(i)"years old"color(white)(a/a)|)))#