MEPV$102$ Practical Example $3\mathrm{.}2-$ Carbon $14$ Dating

A radioactive isotope of an element is a form of the element that is not stable. Instead it spontaneously decays into another element over a period of time. Radioactive decay is an exponential process. If $Q_0$ is the initial quantity of a radioactive substance at time $t=0,$ then the amount of the substance which will be present at any time $t$ in the future is given by:

$Q(t)=Q_0{e}^{-t}$

where $($Lambda$)$ is the radioactive decay constant.

Because radioactive decay occurs at a known rate, it can be used as a clock to measure the time that has elapsed since the decay started. If we know the initial amount of the radioactive material $Q_0$ present in a sample and the amount of material $Q$ left at the current time, we can solve for $t$ in the above mentioned equation to determine how long the decay has been going on$.$ Equation $2\mathrm{.}1$ has practical applications in many areas of science. For example, archaeologists use a radioactive clock based on carbon $14$ to determine the time that has passed since a once living thing died. Carbon $14$ is continually taken into the body while a plant or animal is living, so the amount of it present in the body at the time of death is assumed to be known. The decay constant $$ of carbon $14$ is well known to be $\frac{0\mathrm{.}00012097}{?}$ year. Write a MATLAB program that will prompt the user to enter the percentage of carbon $14$ remaining in a sample and then calculates the age of the sample from it$.$ Displays the results with the correct units by means of the display function in the Command Window.