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.
Percentage of total long term care hours that are provided by unpaid caregivers: 84%. Percentage of Americans over 60 who live with a younger relative: 6.3%. Percentage of Japanese over 60 who do: 70%. Percentage increase by 2040 in the number of elderly requiring long term care that have no children: 50%. Number of centenarians (persons aged 100+) alive today for every one centenarian alive in 1990: 2. Projected number of centenarians in 2050 for every one centenarian alive in 1990: 31.