Question

Carbon-14 is a radioactive element with a half-life of about

5,730 years. Carbon-14 is said to decay exponentially. The decay rate is 0.000121. We start with one gram of carbon-14.

We are interested in the time (years) it takes to decay carbon-14. The distribution for X is ______.

Short answer

This distribution for X is an exponential distribution.

Step-by-step solution

 Definition of exponential distribution

Exponential distribution is a time probability distribution that depends between any kind of events in a Poisson process.

In this case of Poisson Process is a model series of discrete event. Here the average time between event is known but exact time is unknown.

Justification of exponential distribution 

Here in this scenario Carbon-14 is decaying exponentially.

As the carbon-14 is decreasing exponentially, thus the random distribution mass variable of carbon-14 (X) is conveyed through "exponential distribution".