West Dickson

07/14/2023 · Senior High School

The radioactive isotope Chromium- 51 , used to track red blood cells, has a half-life of 27.7 days. Assume an initial amount of 75 mg . 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 day. 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 \( t \) days. \( A(t)= \) c) How long will it take for \( 10 \% \) of the material to decay? Round to the nearest tenth of a day. (HINT: If \( 10 \% \) of the material decays, how much is left?)