solving rational inequalities with a sign chart

Question

Hi, i have 2 application questions about rational inequalities that i hope you will help me solve and explain to me how are they solved:

1)When successful new software is first introduced, the weekly sales generally increase rapidly for a period of time and then begin to decrease. Suppose that the weekly sales S( in thousands of units) tweeks after the software is introduced is given by:
S=200t/(t^2+100) when will the sales be 8 thousand units per week or more?

(my main question here is that should it be >= 8 or >= 8000)

2)A drug is injected into the blood stream of a patient through her right arm. The concentration in the blood stream of the left arm t hours after the injection is given approximetly by:
C=0.12t/(t^2+2) when will the concentration of the drug in the left arm be 0.04 milligram per mililter or greater?


I have solved this one and got as a final answer


x belongs to[1,2]

...is it right?

thanks alot for your help :)

Answer 1

1. It should be >=8. When the variable is defined is defined in thousand of units, you keep it in thousands of units. 

 

2. Yes, you are right. 

C=0.12t/(t^2+2)>=0 is equivalent to (t^2-3t+2)<=0 when you multiply both sides by

(100/4)*(t^2+2) and you can do that without changing the inequality, because it is >0.

 

(t^2-3t+2)<=0 is equivalent to (t-1)(t-2)<=0 and that results in t belongs to [1,2].

 

Hope this helps.

 

Dr. G