## MATH 142: Elements of Calculus II

Present Value Computation using Tables of Integrals

Names:

Work in groups of two to answer the questions below. Put the names of
the people in your group at the top of the page and write your answers
on the page. You may wish to work the problems on scratch paper
before writing your final answer. This will count as one homework assignment.
This project was adapted from question 40 on page 501 of Tan's *Calculus For the Managerial, Life and Social Sciences*.

Elaine purchased a 10-year franchise for a fast food restaurant (for
example, she paid for the right to open a **Friendly's**
restaurant). She estimates that that restaurant will
generate an income of

*R(t) = 250,000 +
2000t*^{2}

dollars/year, where *t* is
the number of years the restaurant has been in operation (i.e. time
*t=0* is now).
- The revenue function is quadratic; its graph is a parabola.
Elaine's prediction is that her revenue will grow slowly for the
first few years and then more rapidly. Do you think this is a
reasonable prediction? If so, why? If not, what do you think would
be more likely?

- If the predicted revenue function is accurate, how long will it take Elaine's revenue to double? Show your work.

- Elaine plans to use the revenue from her restaurant to buy stock
in the franchise. Based on past performance, she estimates that these
stocks will increase in value at 10% per year compounded
continuously. If she is right, what is the present value of the
franchise? (The formula for present value is on page 473 of your
text.)

- If you were Elaine's accountant, how much would you suggest she
offer for the franchise? Why?