For example, ; we need to find y. Then . Raise to both sides keeping in mind that for all . This will give you a linear equation on y. Formally, after finding y, you must check that to make sure that exists because when one raises e to both sides of an equation, one can acquire spurious roots.The age of a machine, x, in years, is related to the probability of breakdown, y, by the formula:
x = 3 + ln(y/1-y)
Determine the probability of breakdown for 1, 3 and 10 years.