The fraction of television sets manufactured by a certain company that are still in working condition after t years of use is approximately $f ( t ) = e ^ { - 0.1 t }$ . What fraction can be expected to fail before 5 years of use? Round your answer to two decimal places, if necessary.
A) 0.61
B) 1.65
C) 0.39
D) 1.00

Question

Quizplus · Accepted Answer

The fraction that fails before 5 years is $1 - f(5) = 1 - e^{-0.1 \times 5} = 1 - e^{-0.5} \approx 0.39$.

The Fraction of Television Sets Manufactured by a Certain Company f(t)=e−0.1tf ( t ) = e ^ { - 0.1 t }f(t)=e−0.1t

The Fraction of Television Sets Manufactured by a Certain Company $f ( t ) = e ^ { - 0.1 t }$