# 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?

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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)|)))#