Radioactivity using an exponential function

Question

A radioactive substance decays according to the equation A(t)= A₀().1)^0.073t, where t is in years and A₀=1 is the original amount of the substance. How long will it take until there is only 10% of the original amount left? Show your work

Answer 1

Substitute A(t) = 0.10A_o. When you do this, you can divide both sides by A_o, simplifying the left side of the equaction to 0.1 (the A_o's will cancel out). Take the log of both sides to solve for t.