Question 1201597
the half life is 5700.
equation for that is 1/2 = (1 + r) ^ 5700
solve for (1 + r) to get (1 + r) = (1/2) ^ (1/5700) = .9998784026.
that's the growth factor per year.
in 5700 years, a present value of 1 is equal to .9998784026 ^ 5700 = .5
if a fossil contains 15% of the carbon-14 that it contained when it was alive, the formmula becomes:
.15 = .9998784026 ^ x
take the log of both sides of the equation to get:
log(.15) = log(.9998784016 ^ x)
this becomes log(.15) = x * log(.9998784026)
solve for x to get x = log(.15) / log(.9998784026) = 15600.70389.
the age of the fossil is 15600.70389 years.
the equation can be graphed as y = .9998784026 ^ x, as shown below.
<img src = "http://theo.x10hosting.com/2023/041002.jpg">