anonymous
  • anonymous
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.
Mathematics
jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
\[9=90e^{-.3t}\] 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 \[\ln(.1)=-.3t\]
anonymous
  • anonymous
finally \[t=-\frac{\ln(.1)}{.3}\]and then a calculator

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