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.
In 1986, private insurers paid nearly 30 percent of the total cost of rehab. Patients paid nearly 14 percent of the total cost that same year. In 2003, however, both patients and insurers paid less for treatment, changing to just over 10 percent and 8 percent, respectively.ven though the cost to the individual patient and his family has declined in recent years, treatment programs often reach into the thousands of dollars. In 2002, the average cost of a rehab treatment program was around $1,400.