Radioactive decay of carbon-14 is used for estimating the age of organic material. The decay is modeled with the exponential function f(t) =f(0)e^kt, where t is time, f(0) is the amount of material at t =0, f(t) is the amount of material at time t, 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 77.45% of the initial (t =0) carbon1 4 is present. Determine the estimated age of the footprint. Solve the prob1 cm by writing a program in a script file. The program firs determines the constant k. then calculates t for f(t) =0.7745f(0), and finally rounds the answer to the nearest year.