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.
Most residential rehabilitation programs last 21-30 days, 8-12 hours per day. Outpatient rehabilitation programs are typically 60-90 days, where patients spend 2-8 hours per day, 2-5 days per week. Desired Results: 1. Sustained elimination of alcohol and other drug use. 2. Improved health and social function. 3. Engagement in continuing care, personal therapy, mutual help groups and/or other healthy lifestyle changes to sustain the improved health and function.