The radioactive isotope Uranium-235, used for nuclear power, has a half-life of 704 million years. Assume an initial amount of 1.7 kg . Use the the formula \( A(t)=A_{0} e^{k t} \) to model the situation, where \( A_{0} \) is the initial amount of the material and \( k \) is a constant representing the rate of decay per million years. a) Find the exact value of \( k \), the decay constant. Round to 6 decimal places or enter an exact answer. \( k= \) b) Using the \( k \) value from part (a), find a function that gives the amount of the isotope \( A \) that remains after \( t \) million years. c) How long will it take for \( 40 \% \) of the material to decay? Round to the nearest tenth of a year. (HINT: If \( 40 \% \) of the material decays, how much is left?) Time:
UpStudy ThothAI Solution
Quick Answer
Step-by-step Solution
Enter your question here…