Answer to Question #272172 in Algebra for Mimi

Question

a) The number of grams of a certain radioactive substance present after t hours is given by the equation Q = Q0e−0.45t, where Q0 represent the ini- tial number of grams. How long will it take 2500 grams to be reduced to 1250.

Answer 1

$\displaystyle \text{Given }\\ Q(t)=Q(0)e^{-0.45t}\\ \text{We solve for t to obtain}\\ e^{-0.45t}=0.5\\ \text{Taking the log of both sides, we have}\\ -0.45t=\ln (0.5)=-0.6931\\ \implies t = 1.54 hrs$