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.
Lengths of stay at a rehabilitation facility vary by individual, but long-term treatment may last anywhere from three months to six months, or longer is some cases. Individuals with more severe forms of addiction or mental illness will require longer stays. The average length of stay for short-term residential treatment was 26 days, while the average length of stay for long-term residential treatment was 70 days, according to 2003 data from the Treatment Episode Data Set.