32. Radioactive decay of carbon-14 is used for estimating the age of organic material. The decay is modeled with the exponential function ()/(0), where r is time, f(0) is the amount of material at 1=0, f() 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 77.45% of the initial (=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 for f()=0.7745/(0), and finally rounds the answer to the nearest year.