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Homework Statement
The technical specification of a particular electrical product states that the probability of its failure with time is given by the function:
f(t) = 1 - ke^(-t/t0) if 0 < t < tmax
f(t) = 0 if t > tmax
where t is the time of service in years, and the constant t0 = 100 years defines the characteristic deterioration time. If the maximal life span of the product tmax is 10 years,
find the value of constant k , explaining its meaning,
Homework Equations
i thought i was supposed to find the integral of 1 - ke^(-t/t0) with respect to t between 0 and 10 years and put the answer equal to 1. then find k from that. [/B]
The Attempt at a Solution
now this is a past exam paper question so i actually have the partial solution to the question which says that:
k = -9/(t0(e^(-10/t0) - 1))
but what i get is k = -9/(t0e^(-10/t0))
I'm pretty sure I'm doing the integral correctly so there must be some step I'm missing that accounts for that extra -1 in the denominator.
[/B]
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