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9 Nov 2021
Given information
Use the following information to answer the next exercises. Carbo is a radioactive element with a half-life of about years. Carbon- is said to decay exponentially. The decay rate is We start with one gram of carbon . We are interested in the time (years) it takes to decay carbon-.
Step-by-step explanation
Step 1.
According to the given information, the random variable follows the exponential distribution with parameter
The cumulative density function of the exponential distribution is given by,
, being the decay parameter.
Therefore,
And
Taking logarithm on both sides of the equation:
Therefore, the value of such that is .
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