Apiece of charcoal is found to contain 30% of the carbon 14 that it originally had. when did the tree die from which the charcoal came? use 5600 years as the half-life of carbon 14.
a(t)=aoe^kt k< 0

Using the equation of half-life, the given is0.5 = e^(5600k) 
in order to solve for k

we then get the log for both sides 
log(0.5) = log(e^(5600k))

then we simplify

log(0.5) = 5600k * log(e) 

k = log(0.5)/(5600*log(e)) 

k = -0.301029996 / (5600*(.434294482)

k = -0.000123776 

Back to the original equation, we have
0.3 = 1*e^(k*t)

where we substitute for k
0.3 = e^(-.000123776*t) 

and then get the log for each
log(0.3) = log(e^(-.000123776*t))

and then simplify

log(0.3) = -.000123776*t*log(e)

and then solve for t

t = log(0.3) / (-.000123776*log(e)) 

t = 9727 years

That is when the tree died.

Standing in the sunlight and feeling the heat on your face (uv radiation is entering the skin, converting to infrared radiation, and is absorbed by your tissues)orstanding near a fire and feeling the heat on your skin (infrared radiation transfer)