The reliability of a new model of CD player can be described by the exponential function R(t) = 2.7-(1/3)t, where the reliability R is the probability (as a decimal) that the CD player is still working t years after it is manufactured. Round the answer to the nearest hundredth. Then write your answer as a percent.
-What is the probability that the CD player will still work 5 years after it is manufactured?
A) 1%
B) 94%
C) 19%
D) 7%

Question

Quizplus · Accepted Answer

To find the probability that the CD player will still work 5 years after it is manufactured, substitute t = 5 into the given function: R(5) = 2.7 - (1/3)*5 = 2.7 - 5/3 = 2.7 - 1.67 = 1.03. Since probabilities cannot exceed 1, this suggests a mistake in the formulation of the problem or in the interpretation of the function. However, treating the function correctly as likely intended to describe a decay within a 0 to 1 range, the calculation error needs to be corrected. The correct approach, assuming a typo in the function provided, would involve a function that actually yields a probability between 0 and 1 for a given time. Without the correct function, we cannot accurately calculate the probability, but the intended process involves substituting the time into the correct reliability function, calculating the result, and converting it to a percentage. Given the options and the mistake in the problem statement, none of the provided choices can be accurately derived from the given function.

The Reliability of a New Model of CD Player Can