A farmer in china discovers a mammal hide that contains 54% of its original amount of c-14. Find the age of the mammal hide to the nearest year

Answer:6163.2 yearsStep-by-step explanation:The formula we use for evaluating the C 14 decay is[tex]A_t=A_0e^{-kt}[/tex]Where[tex]A_t[/tex]=Amount of C 14 after “t” year[tex]A_0[/tex]= Initial Amountt= No. of yearsk=constantIn our problem we are given that [tex]A_t[/tex] is 54% that is if [tex]A_0=1[/tex] , [tex]A_t=0.54[/tex]Also , k=0.0001We have to find t=?Let us substitute these values in the formula[tex]0.54=1* e^{-0.0001t}[/tex]Taking log on both sides to the base 10 we get[tex]log 0.54=log e^{-0.0001t}[/tex][tex]-0.267606 = -0.0001t*log e[/tex][tex]-0.267606 = -0.0001t*0.4342[/tex][tex]t=\frac{-0.267606}{-0.0001*0.4342}[/tex][tex]t=6163.20[/tex]t=6163.20 years