# Radiometric dating calculus equations

The last figure I heard was that there are currently eight nuclear subs on our ocean floors. It doesn't work for sea creatures and other things that are under water. Then they measure how much is left in the specimen when they find it. It comes from cosmic rays that rain down on the earth (and us) from outer space.Radiocarbon dating can be used on samples of bone, cloth, wood and plant fibers.The half-life of a radioactive isotope describes the amount of time that it takes half of the isotope in a sample to decay.

The exponential decay formula is given by: $$m(t) = m_0 e^$$ where $\displaystyle r = \frac$, $h$ = half-life of Carbon-14 = 30$ years, $m_0$ is of the initial mass of the radioactive substance.

It’s the time it takes for a batch of radioactive atoms to decay away, i.e. We can relate \(\tau_\) to \(\lambda\) easily using the formula derived above.

We just say we start with \(N_0=100\) atoms and calculate the \(t\) it takes for this to drop to \(N=50\).

WARNING: there is a little bit of calculus involved.

We start by noting that the speed of radioactive decays occurring in a sample is proportional to the number of radioactive atoms in the sample. If you had 10 jumping beans and saw one jump every second, you’d expect to see about 10 jumps per second if you had 100.