Radioactive decay of carbon$-14$ is used for estimating the age of organic material. The decay is modeled with the exponential function so$=10$e$",$ where r is time, f$(0)$ is the amount of material at r$=0.$ roo is the amount of material at time $1,$ and k is a constant. Carbon$-14$ has a half$-$life of approximately $5,730$ years. A sample taken from the ancient footprints of Acahualinca in Nicaragua shows that $77\mathrm{.}45\%$ of the initial $(1=0)$ carbon$-14$ is present. Determine the estimated age of the footprint. Solve the prob$-$ lem by writing a program in a script file. The program first determines the constant k$,$ then calculates e for S$()=0\mathrm{.}7745/(0),$ and finally rounds the answer to the nearest year.