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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/t

_{0}) if 0 < t < t

_{max}

f(t) = 0 if t > t

_{max}

where t is the time of service in years, and the constant t

_{0}= 100 years defines the characteristic deterioration time. If the maximal life span of the product t

_{max}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/t

_{0}) 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/(t

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.

k = -9/(t

_{0}(**e^(-10/t**_{0}) - 1))**but what i get is k =****-9/(t**_{0}**e^(-10/t**_{0}))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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