The fraction of television sets manufactured by a certain company that are still in working condition after t years of use is approximately $f ( t ) = e ^ { - 0.2 t }$ .What fraction can be expected to fail before 2 years of use? Round your answer to two decimal places,if necessary.
A)1.49
B)0.91
C)0.67
D)0.33

Question

Quizplus · Accepted Answer

To find the fraction that fails before 2 years, we subtract the fraction that are still working after 2 years from 1. For $t = 2$, $f(2) = e^{-0.2 \times 2} = e^{-0.4}$. Calculating $e^{-0.4}$ gives approximately 0.67, so the fraction that fails is $1 - 0.67 = 0.33$.

The Fraction of Television Sets Manufactured by a Certain Company f(t)=e−0.2tf ( t ) = e ^ { - 0.2 t }f(t)=e−0.2t

The Fraction of Television Sets Manufactured by a Certain Company $f ( t ) = e ^ { - 0.2 t }$