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.
Recent studies have shownthat after 6 months, treatment for alcoholism is successful for 40to 70 percent of patients, cocaine treatment is successful for 50 to60 percent, and opiate treatment is successful for 50 to 80 percent,with effectiveness defined as a 50-percent reduction in substanceuse after 6 months.