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.
10 %: The percentage of people who enter a nursing home who will stay there five or more years. 65% : The percentage of people who entered a nursing home who died within one year of admission. Five months: The typical length of nursing-home stay for patients who eventually died in the nursing home. million: The number of Americans over age 65 who need long-term care in 2012. 12 million: The number of Americans expected to need long-term care in 2020. 40% : The percentage of the older population with long-term care needs who are poor or near-poor (income below 150% of the federal poverty level).