Question

The mass m(t) remaining after t years from a 90-gram sample of a radioactive element is given by m(t)=90e^-0.3t. When will the mass remaining equal 9 grams? Round your answer to the nearest hundredth of a year.

Answer 1

\[9=90e^{-.3t}\] we solve for \(t\)
divide by 90 get
\[\frac{1}{10}=e^{-.3t}\] or if you prefer
\[.1=e^{-.3t}\] then in log form this means
\[\ln(.1)=-.3t\]

Answer 2

finally
\[t=-\frac{\ln(.1)}{.3}\]and then a calculator