Rational function Question

[Crookshanks]

I don't have problems doing this up until part e. So I will give you what I have so far. Is part e trying to find out what t is if C(t) = 10, 15, 20, etc... ? How do I find that with a rational function?


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 - 10000t
---------------------
t^2 - 10t + 25

What does the graph of the function look like? To answer this question, find:
a. The vertical asymptotes, if any:
t^2 - 10t + 25 = 0
(t-5)(t-5)
t = -5
answer: -5

b. The horizontal asymptote, if any:
The degree of 1000t^2 and t^2 are both the degree of 2. The theorem of horizontal aymptotes stats that the line y = 1000/1 is the horizontal asymptote of C.

c. The t intercepts, if any:
C(t) = 1000(25) + 50000
= 25000 + 50000 75000
------------------- = -------------
25 + 50 + 25 100
C(t) = 750 and t intercept = 750

d. The C intercept, if any:
unknown

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

 

[Gene]

a) Close, but if (t-5) = 0 then t=5
b) Looks good
c) I don't think so. The vertical asymptote is not an intercept. They occur when C(t) = 0
1000t^2 - 5000t = 0
(The denominator doesn't matter. It goes away by multiplying by it.)
There is one at C(0). Find the other.
Hint: If you want to type things like that click the C(ode) button twice then type betweeen the boxes. That keeps your spascing from vanishing.

1000(25) + 50000      25000 + 50000
------------------- = -------------
  25 + 50 + 25              100

d) The C intercept is when t = 0

e) You have done the calculations for these before.

         1000*(10)^2-10000*(10)
C(10) = ----------------------
           (10)^2-10*(10)+25

etc.