The revenue for Dell Computer Corporation from 1985 through 1993 can be modeled by the equation y= 42.757(1.7070)^x where x is the time in years with x = 0 corresponding
to 1985, and y is the revenue in millions of dollars.
Exercises
1. Use the model y= 42.757(1.7070)^x to answer the following questions.
(a) What was Dell Computer Corporation's revenue in 1985?
(b) What was Dell Computer Corporation's revenue in 1992?
(c) In what year was the revenue approximately $3 billion?
2. Find the inverse function of y= 42.757(1.7070)^x. What does the inverse function represent?
3. Use the inverse function you wrote in Exercise 2 to determine the year when
revenue was approximately $3 billion. Compare this to your answer from
Exercise 1.
4. Differentiate y= 42.757(1.7070)^x
5. What is the rate of change of revenue in 1985? in 1988?
6. Because the revenue follows an exponential growth model, what is true about the
revenue’s rate of change over time? Explain.
7. Set up a definite integral to determine the total revenue from 1985 through 1993.
8. Evaluate the integral you wrote in Exercise 7 to determine the total revenue from
1985 through 1993.
9. Determine the average monthly revenue from 1985 through 1993.
10. Assuming there are 52 weeks in a year, determine the average weekly revenue from
1985 through 1993.
11. Assuming there are 365 days in a year, determine the average daily revenue from
1985 through 1993.
12. If the revenue continued to follow the same growth model, what would the revenue
be in 2006?
13. Based on your answer to Exercise 12, what is the likelihood that the revenue continues
to follow this growth model? Explain.
14. Use the Internet to find Dell Computer Corporation’s actual revenue in 2006.
15. Based on your findings in Exercises 12 and 14, what conclusions can you make about
the growth of the revenue? Does the revenue continue to increase? Does the rate of change
continue to increase? Explain.