NEED HELP ON NUMBER 13 AND 141.A psychologist finds that the response to a certain stimulus varies with age groupaccording toR= y^4 +2y^3 - 4y^2 -5y +14,- where R is response in microseconds and y is age group in years. For what agegroup is the response equal to 8 microseconds?2. The profit of a football club after a takeover is modelled byp(t)=t^3 -14t^2 +20t +120,where t is the number of years after the takeover. In which years was the clubmaking a loss?​

Accepted Solution

Answer:Question 13: For age groups y=1 and y=1.3 response is 8 microseconds.Question 14: The club was making a loss between 11.28 and 4.88 years.Step-by-step explanation:Question 13:The age group y for which the response rate R is 8 microseconds  is given by the solution of the equation[tex]8=y^4 +2y^3 - 4y^2 -5y +14.[/tex]We graph this equation and find the solutions to be[tex]y=1;[/tex]   [tex]y=1.302;[/tex]     [tex]y=-2;[/tex]    [tex]y=-2.302.[/tex]Since only positive solutions for y are valid in the real world we take only those.Thus only for age groups y=1 and y=1.3 the response is 8 microseconds.Question 14:The footbal club is making a loss when [tex]p(t)<0.[/tex]Or [tex]t^3 -14t^2 +20t +120<0.[/tex]We graph this inequality and find the solutions to be [tex]t<-2.17[/tex] and [tex]4.88<t<11.28.[/tex]Since in the real world only positive values for t are valid, we take the the second solution to be true.Thus the club was making a loss in years [tex]4.88<t<11.28.[/tex]