The percentage of a certain brand of computer chips that will fail after t years of use is estimated to be
P(t) = 100(1 − e−0.12t ).
What percentage of this brand of computer chips are expected to be usable after 3 years? (Round your answer to one decimal place.)
P(t) = 100(1-e^-0.12*3)
P(3) = 100(1-0.6977) = 30.23% Fails.
100% - 30.23% = 69.7% Usable.
To find the percentage of computer chips that are expected to be usable after 3 years, we need to evaluate the function P(t) at t = 3.
Given P(t) = 100(1 − e^(-0.12t)), we can substitute t = 3 into the equation:
P(3) = 100(1 − e^(-0.12(3)))
First, we calculate -0.12(3) = -0.36 and then e^(-0.36) using a calculator:
e^(-0.36) ≈ 0.6988
Now, substitute this value back into the equation:
P(3) = 100(1 − 0.6988)
Next, subtract 0.6988 from 1:
P(3) = 100(0.3012)
Finally, multiply 100 by 0.3012:
P(3) ≈ 30.12
Therefore, approximately 30.12% of this brand of computer chips are expected to be usable after 3 years.