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Question 91088: this is possibly the harderst proble I have ever seen in my life. Please help me. I have such a difficult time with word problems. Please help me with this so I can get on with the rest of my math. I really appreciate your help
This problem set involves a formula (a rational function) with which a new tortilla company might be able to forecast its production over the first few weeks of operation.
In this formula, C(t) is the number of bags of tortillas that can be produced per week after t weeks of production.
Here is the rational function that was developed to best describe the fledgling company's production.
c (t)= 1000t^2 -10,000t / t^2-10t+25
What does the graph of the function look like? To answer this question, find
a. The vertical asymptotes, if any:
b. The horizontal asymptote, if any:
c. The t intercepts, if any:
d. The C intercept, if any:
e. The value of C(t) at:
t = 10 weeks
t = 15 weeks
t = 20 weeks
t = 25 weeks
t = 30 weeks
t = 35 weeks
Show your calculations
f. The value of C(t) at:
t = -5
t = -10
What is the projected maximum number of bags of tortillas that the company can never exceed? Discuss this answer in terms of the horizontal asymptote.
3. Can the company reach that maximum? If so, after how long
4. Give an interpretation of what might be happening to the company's production efforts from week 5 to week 10? Discuss this answer in detail.
5. In terms of the business application, is there any meaning for the value of C(t) when t = -5 and t = -10? Explain your answer.
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! C(t) is the number of bags of tortillas that can be produced per week after t weeks of production.
Here is the rational function that was developed to best describe the fledgling company's production.
c (t)= 1000t^2 -10,000t / t^2-10t+25
What does the graph of the function look like?
-------------
To answer this question, find
a. The vertical asymptotes: t=5
--------------------
b. The horizontal asymptote:t = 1000
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c. The t intercepts, if any:
Let C(t) = 0; solve for t as follows:
1000t^2-10000t = 0
1000t(t-10) = 0
t-intercepts at t=0 and at t=10
-------------------------
d. The C intercept, if any:
Let t=0 then C(0)=0
--------------------------
I'll leave the following to you.
e. The value of C(t) at:
t = 10 weeks
t = 15 weeks
t = 20 weeks
t = 25 weeks
t = 30 weeks
t = 35 weeks
Show your calculations
f. The value of C(t) at:
t = -5
t = -10
What is the projected maximum number of bags of tortillas that the company can never exceed? Discuss this answer in terms of the horizontal asymptote.
C(t) can never reach or exceed 1000
------------------------
3. Can the company reach that maximum? If so, after how long
No, 1000 is an asymtotic value; C(t) is always < 1000
------------------------
4. Give an interpretation of what might be happening to the company's production efforts from week 5 to week 10? Discuss this answer in detail.
During that interval C(t)<0 but increasing.
-------------------
5. In terms of the business application, is there any meaning for the value of C(t) when t = -5 and t = -10? Explain your answer.
It might model the production before t=0; or it might be meaningless
if the company did not exist during those weeks.
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Cheers,
Stan H.
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