Direction field analysis Consider the general first-order initial value problem \(y^{\prime}(t)=a y+b\), \(y(0)=y_{0}\), for \(t \geq 0\), where a, b, and v0 are real numbers.
a. Explain why y = -b/a is an equilibrium solution and corresponds to a horizontal line in the direction field.
b. Draw a representative direction field in the case that a > 0. Show that if \(y_{0}>-b / a\), then the solution increases for \(t \geq 0\), and if \(y_{0}<-b / a\), then the solution decreases for \(t \geq 0\).
c. Draw a representative direction field in the case that a > 0. Show that if \(y_{0}>-b / a\), then the solution decreases for \(t \geq 0\), and if \(y_{0}<-b / a\), then the solution increases for \(t \geq 0\).
Leslie Ogu PSYC 2012 03/02/2016 Group Processes Pt. 1 Characteristics of Groups ➢ 2 or more people ➢ Interactions are interdependent and influence each other ➢ Help basic human needs to belong, get information, establish our identity, and social norms ➢ Members tend to be similar to one another ○ This is usually due to the group one belongs to having an impact on who you are if you spend enough time with them ○ Adapting to the culture Deindividuation ➢ Why do people behave differently in crowds ➢ Def: the loosening of normal constraints on behavior when in a crowd, leading to an increase in impulsive and deviant acts ○ When we are around large numbers of people, we tend to get a little crazier because we are less wary of the consequences (since the group is so large) ➢ When people become deindividuated, normal constraints against deviant behavior is lessened ○ Feel less accountable for actions (more excuses) ○ ** Deindividuation does not require facetoface contact ** ■ Ex: internet, social media ➢ Factors affecting deindividuation ○ Group Size ■ The larger the group, the more deindividuated people become ● they feel less accountable because it’s harder to single one person out ○ Anonymity ■ The more anonym
