How are these concepts of direct, inverse, and joint variation used in everyday life? Provide examples for each.
1) Direct variation -- as the independent variable increases so does the dependent variable.
The amount of money a person who is paid hourly makes varies directly with the number of hours worked.
P=kh where P is the pay, h the number of hours, and k, the proportionality constant, is the hourly wage.
2) Inverse variation -- as the independent variable increases, the dependent variable decreases or vice versa.
The worth of a car varies inversely with its age.
`W=k/a` where W is the worth of a car at age a and k is the proportionality constant.
3) Joint variation -- the dependent variable varies directly with two or more independent variables.
The gravitational pull between two objects varies jointly with their masses and inversely with the square of the distance between them.
`F=g(m_1m_2)/d^2` where g is the gravitational constant.
Let's say a family husband is working, so if more people works in family, more income for the family. It is an example of direct variation.
If family has less members, more saving (provided that the family has the same amount of income). More members, less saving ( income is still the same). It is an inverse variation.
more members work = more earning in family
more members = less saving in family
More members is in joint variation to earning and saving.