When we write vectors as matrices, we tend to write an $n$-dimensional vector vector as $n \times 1$ column matrix. We emphasize that the gradient vector is defined only for scalar-valued functions. For vector valued functions, we will stick with viewing the derivative as a matrix.
Gloomy Addiction Relapse Statistics. Drug and alcohol rehab statistics show that the percentage of people who will relapse after a period recovery ranges from 50% to 90%. This is a frightening statistic and it is often used as justification for those who wish to carry on with their addiction.
Alcohol rehabilitation duration and average time. The average time spent in a typical inpatient rehab program is roughly one month. Long-term residential treatment can take several months to complete. Time spent in outpatient alcohol rehabilitation can be extended to a year, or more, although an average session is 10-12 weeks long.