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.)
See previous post.
To find the percentage of this brand of computer chips that are expected to be usable after 3 years, we can substitute t = 3 into the given function P(t) = 100(1 − e^(-0.12t)) and evaluate it.
Let's calculate step by step:
Step 1: Substitute t = 3 into the function P(t):
P(3) = 100(1 − e^(-0.12 * 3))
Step 2: Simplify the expression inside the parentheses:
P(3) = 100(1 − e^(-0.36))
Step 3: Calculate the exponent:
P(3) = 100(1 − 0.6988057)
Step 4: Subtract the result from 1:
P(3) = 100(1 - 0.6988057) = 100(0.3011943)
Step 5: Multiply the result by 100 to convert to a percentage:
P(3) = 30.11943%
Therefore, approximately 30.1% (rounded to one decimal place) of this brand of computer chips are expected to be usable after 3 years.