Exam 1: Functions and Change

Harley Davidson (ticker symbol HOG) stock prices dropped sharply in late 2008. Series 1 in the graph below shows the actual prices at the end of each week. The trend over time is approximately linear; and the graph of a possible linear model is given by Series 2. Based on the data given, find the linear model and use it to approximate the stock's price on November 30, 2008, assuming the current trend continued.

Bank A offers 12% interest, compounded yearly, and Bank B offers 11.1% interest, compounded continuously. Which bank should you choose if you have $1000 to invest for 10 years?

The table gives information about the number of cases of pancreatic cancer diagnosed in the United States. A) Find the average rate of change in number of cases from 1997 to 2002. B) Find the average rate of change in number of cases from 2002 to 2004. C) Is the average rate of change increasing or decreasing?

Solve for t. Round to two decimal places.

Find the average rate of change of between t = 1 and t = 3. Round to two decimal places.

A furniture moving company charges a fixed amount plus a charge for each pound that they move. A person who shipped 60 pounds of furniture was charged $280, while someone else was charged $610 to ship 170 pounds. A. Write a function that represents the moving cost, C, in terms of pounds, x, and fixed cost. B. Suppose the company changes their rates. They increase the per pound charge by $1 but cut the fixed amount they charge by half. What is the new function that represents the new moving cost, D? C. Will someone who ships 170 pounds pay more or less with the new rates than they would have with the original rates?

A population is growing according to the formula . What is the population in year 9?

Write a function that represents the following situation. The gravitational force, F, between two bodies is inversely proportional to the square of the distance, d, between them.

The equation of the line through the points (1, 2) and (-1, -4) is:

The function represents exponential growth or decay. A. What is the initial quantity? B. What is the initial growth or decay rate?

If defines the function graphed in the following figure, then A =_____, B =_____, and C =_____.

What value of B would you use if was to model a periodic function with period 1 year where t is measured in months? Round to 4 decimal places.

Given the function , find and simplify .

If defines the function graphed in the following figure, then A =_____, B =_____, and C =_____.

A textbook company had fixed costs of $15,000 and variable costs of $20 for a certain book. The company sells the books for $30 each. Find a formula for the profit function, .

Lisinopril is an ACE inhibitor derived from the venom of a Brazilian pit viper frequently used in the treatment of hypertension. Because of Lisinopril's relatively long half-life of 12 hours, patients need to take a dose just once per day. A patient takes his first dose, 20 mg, at 6 pm on Saturday. a) How many hours does it take for the amount of Lisinopril in the patient's body to decrease to 17 mg? Round to two decimal places. b) How many milligrams remain in the patient's body right before he takes his next 20 mg at 6 pm on Sunday? Round to two decimal places

The population of the United States in millions t years after 1790 during the period from 1790 to 1860 was given approximately by the exponential formula . What was the annual percent growth rate of the US during this time period?

One of the graphs below shows the rate of flow, R, of blood from the heart in a man who bicycles for 20 minutes, starting at t = 0 minutes. The other graph shows the pressure, p, in the artery leading to a man's lungs as a function of the rate of flow of blood from the heart. Estimate .

A school library opened in 1980. In January of 2000, they had 33,000 books. One year later, they had 33,240 books. Assume they acquire the same number of books at the start of each month. A. How many books did they have in January of 2003? B. How many books did they have in July of 1980?

As , _____.