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# solving rational inequalities with a sign chart

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 :)

### 1 Answer by Expert Tutors

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Hediye G. | Experienced, Patient College Professor/ TutorExperienced, Patient College Professor/ ...
4.8 4.8 (294 lesson ratings) (294)
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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