Question

NEED HELP ON NUMBER 13 AND 14
1.
A psychologist finds that the response to a certain stimulus varies with age group
according to
R= y^4 +2y^3 - 4y^2 -5y +14,
- where R is response in microseconds and y is age group in years. For what age
group is the response equal to 8 microseconds?
2. The profit of a football club after a takeover is modelled by
p(t)=t^3 -14t^2 +20t +120,
where t is the number of years after the takeover. In which years was the club
making a loss?​

Answer 1

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

$8=y^4 +2y^3 - 4y^2 -5y +14.$

We graph this equation and find the solutions to be

$y=1;$   $y=1.302;$     $y=-2;$    $y=-2.302.$

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 $p(t)<0.$

Or

$t^3 -14t^2 +20t +120<0.$

We graph this inequality and find the solutions to be

$t<-2.17$ and $4.88<t<11.28.$

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 $4.88<t<11.28.$