linen scrolls contain 80.9% of Carbon-14. how old are the scrolls if the half-life for deacy is 5.73X10^3??
plz tell me what type of equation to use.
ln(M/Mo) = -kt
ln = natural log
M = mass left (not needed)
Mo = original mass (not needed)
(M/Mo) = 0.809
k = 0.693/T(half)
T(half) = 5.73X10^3 years.
ln(M/Mo) = -kt
ln = natural log
M = mass left (not needed)
Mo = original mass (not needed)
(M/Mo) = 0.809
k = 0.693/T(half)
T(half) = 5.73X10^3 years.
ln(M/Mo) = -kt
ln = natural log
M = mass left (not needed)
Mo = original mass (not needed)
(M/Mo) = 0.809
k = 0.693/T(half)
T(half) = 5.73X10^3 years.
To determine the age of the scrolls, we can use the equation for exponential decay. The equation is:
N(t) = N(0) * (1/2)^(t / T)
Where:
N(t) is the remaining percentage of Carbon-14 at time t
N(0) is the initial percentage of Carbon-14 (in this case, 80.9%)
t is the time that has passed
T is the half-life of Carbon-14 (in this case, 5.73 x 10^3 years)
Now, let's solve for t:
N(t) = N(0) * (1/2)^(t / T)
We know that N(t) is 80.9% or 0.809, and N(0) is 1. Substitute these values into the equation:
0.809 = 1 * (1/2)^(t / 5.73 x 10^3)
Next, rearrange the equation to solve for t:
(1/2)^(t / 5.73 x 10^3) = 0.809
Take the logarithm of both sides of the equation:
log((1/2)^(t / 5.73 x 10^3)) = log(0.809)
Using the logarithm property:
(t / 5.73 x 10^3) * log(1/2) = log(0.809)
Now, solve for t by isolating it:
t = (log(0.809)) / (log(1/2)) * 5.73 x 10^3
Using a scientific calculator or math software, calculate the right side of the equation to obtain the value of t, which will give you the age of the scrolls.