Exam 2: Nonlinear Functions and Models

The U.S. population was 180 million in 1960 and 240 million in 1990. Assuming exponential population growth, what will the population be in the year 2020? Round your answer to the nearest million. __________ million

You are the sales manager for Montevideo Productions, Inc., and you are planning to review the prices you charge clients for television advertisement development. You currently charge each client an hourly development fee of $2,000. With this pricing structure, the demand, measured by the number of contracts Montevideo signs per month, is 25 contracts. This is down 10 contracts from the figure last year, when your company charged only $1,000. Construct a linear demand equation giving the number of contracts q as a function of the hourly fee p Montevideo Productions, Inc., charges for development.

The market research department of the Better Baby Buggy Co. predicts that the demand equation for its buggies is given by where q is the number of buggies it can sell in a month if the price is $ x per buggy. What is the largest monthly revenue?

Find N , A , and b for the function.

You have just opened a new nightclub, Russ's Techno Pitstop, but you are unsure how much to charge for the cover charge (entrance fee). One week you charged $7 cover per guest and averaged 339 guests per night. The next week you charged $16 per guest and averaged 222 guests per night. Find the linear demand equation showing the number of guests q per night as a function of the cover charge p .

Find the logistic function with the given properties. has limiting value 8 and passes through (0, 2)and (1, 6).

The table below is filled correctly. Exponential form Logarithmic form

Find an equation for exponential function that passes through the pair of points and . ( )

Which of the following three functions will be largest for large values of x ? Select the correct answer.

The given table corresponds to the function .

Model the data using an exponential function .

Plutonium-239 is used as a fuel for some nuclear reactors and also as the fissionable material in atomic bombs. It has a half-life of 24400 years. How long will it take 20 grams of plutonium-239 to decay to 3 grams? Round your answer to the nearest year. __________ years

Use logarithms to solve the equation. (Round answers to four decimal places.)

Soon after taking an aspirin, a patient has absorbed 330 mg of the drug. If the amount of aspirin in the bloodstream decays exponentially with half being removed every 3 hours, find the amount of aspirin in the bloodstream after 7 hours. Select the correct answer.

The two fraternities Sigma Alpha Mu and Ep Sig plan to raise money jointly to benefit homeless people on Long Island. They will sell Starship Troopers T-shirts in the Student Center, but they are not sure how much to charge. Sigma Alpha Mu treasurer Solo recalls that they once sold 200 shirts in a week at $8 each, but Ep Sig treasurer Justino claims that, based on past experience, they can sell 500 per week if they charge $4 each. The university administration charges the fraternities $300 per week for use of the Student Center. What is the largest possible weekly profit, rounded to the nearest dollar?

Use logarithms to solve the equation. (Round answers to four decimal places.) x = __________

The chart shows the number of research articles in the prominent journal Physics Review that were written by researchers in Europe during 1983-2003 ( represents 1983). Year, t 0 5 10 15 20 Research Articles, A (1,000)1.2 2.1 3.8 5.1 5.7 What is the logistic regression model for the data? (Round all coefficients to two significant digits.) At what value does the model predict that the number of research articles will level off? __________ articles According to the model, how many Physics Review articles were published by U.S. researchers in 1990 ( )? __________ articles

Graph the function.

Model the data using an exponential function . Select the correct answer.

The given table corresponds to the function .