Hello, I need help with this problem: Radioactive materials decay to a non-radioactive state in a certain amount of time. The 'half-life' of a radioactive material is the amount of time for the material to decay to half its starting value. The amount of radioactive material left after t years is often modeled by the following equation:

r ( t ) - Ae - Ket where e is Fuler's number ( = 2. 718 ) and K - In ( 2 ) half - life* Calculate r ( t ) and show that it is proportional tor ( t ) . In other words , show that r ( t ) = cr ( t ) for some constant C . How is crelated to the initial amount of material ( + ( O ) ) and K ? The half-live of carbon - 14 ( which is radioactive and often used in dating ancient artifacts ) decays into non - radioactive nitrogen - 14 in approximately 5. 730 years ." How much carbon - 14 remains from an initial pure sample after 2000 years ? How much time is required to decay to 10 % of the initial amount