The amount of carbon-14 still present in a sample after t years is given by the function
where C0 is the initial amount. Estimate the age of a sample of wood discovered by an archeologist if the carbon level in the sample is only 18% of its original carbon-14 level.
I did one for you. Now you do this one.
By the way you left the half life of carbon 14 or exponential decay function out of your statement of the problem making it impossible without looking that up.
To estimate the age of the sample of wood, we need to use the given information about the carbon level in the sample.
The function that represents the amount of carbon-14 still present in a sample after time t is given by:
C(t) = C0 * (1/2)^(t/T)
In this equation, C(t) represents the amount of carbon-14 still present in the sample after time t, C0 represents the initial amount of carbon-14, and T represents the half-life of carbon-14.
We are told that the carbon level in the sample is only 18% of its original carbon-14 level. We can set up the following equation to solve for the time t:
0.18 * C0 = C0 * (1/2)^(t/T)
Now, let's solve for t:
0.18 = (1/2)^(t/T)
To solve for t, we need to take the logarithm of both sides of the equation. We can use the natural logarithm (ln) or the logarithm to any base:
ln(0.18) = ln((1/2)^(t/T))
Using the logarithm property of exponents, we can bring down the exponent t/T:
ln(0.18) = (t/T) * ln(1/2)
Now, we can solve for t by multiplying both sides by T and dividing by ln(1/2):
t = (ln(0.18) * T) / ln(1/2)
Substituting the known value for T (the half-life of carbon-14), we can calculate the estimated age of the sample of wood.