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)ekt, 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) carbon-14 is present. Determine the estimated age of the footprint. Solve the problem by writing a program in a script file. The program first determines the constant k, then calculates t for f(t) = 0.7745f(0), and finally rounds the answer to the nearest year.