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Business math application

I have attached the questions.

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.

1. 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

2. 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.


Solution Summary

This provides an example of working with algebra in a given business situation, including maximum and asymptote, and working with functions.