A statistical study indicates that the fraction of the can openers manufactured by a certain company that are still in working condition after t years of use is approximately $f ( t ) = e ^ { - 0.3 t }$ . The fraction that can be expected to fail during the 2nd year of use is about $\frac { 19 } { 100 }$ .

Question

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The fraction still working after 1 year is $f(1) = e^{-0.3(1)} = e^{-0.3}$, and after 2 years is $f(2) = e^{-0.3(2)} = e^{-0.6}$. The fraction that fails during the 2nd year is the difference: $e^{-0.3} - e^{-0.6}$. Calculating this gives approximately 0.19, or $\frac{19}{100}$.

A Statistical Study Indicates That the Fraction of the Can f(t)=e−0.3tf ( t ) = e ^ { - 0.3 t }f(t)=e−0.3t

A Statistical Study Indicates That the Fraction of the Can $f ( t ) = e ^ { - 0.3 t }$