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−0.1t ).
What percentage of this brand of computer chips are expected to be usable after 6 years? (Round your answer to one decimal place.)
___ %
Precentate usable=100- percentage filed
= 100-100(1-e^-.1t)=100e^-.1t
at t=6
percentage usable=100e^-.6=54.9percent
Thanks!
To find the percentage of this brand of computer chips that are expected to be usable after 6 years, we need to evaluate the function P(t) at t = 6.
First, let's substitute t = 6 into the function P(t):
P(6) = 100(1 − e^(-0.1 * 6))
Next, we need to calculate e^(-0.1 * 6).
Using a calculator or a math software, we find that e^(-0.1 * 6) ≈ 0.6065.
Now, substitute this value back into the original formula:
P(6) = 100(1 − 0.6065) = 100(0.3935) ≈ 39.35
Therefore, the percentage of this brand of computer chips that are expected to be usable after 6 years is approximately 39.35%.