Exam 1: Functions and Change

The demand and supply curves for a certain product are given in terms of price, p, by and . What is the equilibrium quantity?

Does represent exponential growth or decay?

Solve using logs. Round your answer to 3 decimal places.

If the size of a bacteria colony doubles in 8 hours, how many hours will it take for the number of bacteria to be 11 times the original amount? Round to 2 decimal places.

Find an equation for the line L shown. Your answer will contain the positive constant b.

A photocopy machine can reduce copies to 90% or 70% of their original size. By copying an already reduced copy, further reductions can be made. Which will be larger, an image that has been reduced on the 90% setting 10 times, or the same image after being reduced 3 times on the 70% setting?

What is the equation for the graph obtained by shifting the graph of vertically upward by 7 units, followed by vertically stretching the graph by a factor of 5?

You have $500 invested in an account earning 7.2% interest compounded annually. How many years will it take to triple your money? Round to the nearest tenth of a year.

Write a formula for the population, P, as a function of time, t, if the population starts at 9000 and grows by 125 people each year.

The following figure gives both supply and demand curves for a certain product. If the price is $75 per item, would you expect the market pressures to push the price higher or lower?

Write a formula for the population, P, as a function of time, t, if the population starts at 6000 and grows by 10% each year.

Values for g(x) are given in the following table. Does it appear that g(x) is concave up or concave down?

Assume that the function shown in the following table is periodic. What is the amplitude of the function?

In 1992, the Population Crisis Committee wrote: "Large cities in developing countries are growing much faster than cities in the industrialized world ever have. London, which in 1810 became the first industrialized city to top 1 million, now has a population of 11 million. By contrast, Mexico City's population stood at only a million just 50 years ago and now it is 20 million." Assume that the percentage growth rates of London and Mexico City were constant over the last two centuries. How many times greater is Mexico City's percentage growth rate than London's? Round to the nearest tenth.

If , find and simplify the average rate of change .

You were the housing minister in the year 1996 for a country with 30 million people. You were asked to predict the population 15 years from 1996 as part of a 15 year master plan for housing. Census records show that the population was 22.684 million in 1986 and 26.087 million in 1991. What was your best prediction of the population 15 years from 1996?

Tornados are classified in several ways. A tornado's classification on the Fujita Scale as F1 through F5 is most commonly cited. Another classification of tornados is by path length, given by the formula where L is the length of the tornado's path length, in miles. The Binger, Oklahoma tornado of 1981 was an F4 whose path was 16 miles in length. What was its Pl classification?

Delia runs 3.1 miles from home to the park at 6 mph, jumps on her bike and returns home in 12 minutes. A. Sketch a well-labeled graph of Delia's distance from home as a function of time. B. Find the slope of each segment of the graph and interpret their meaning. C. What does it mean to say that Delia's velocity on the way home is inversely proportional to the time she takes to ride home?

A premium ice cream company finds that at a price of $5.50, demand for their ice cream cones is 2500. For each $0.25 increase in price, the demand decreases by 50. Graph the revenue function and find the price that will maximize revenue.

The height (in inches) and weight (in pounds) of 8 students is given in the following table. Find a regression line for this data and use it to estimate the weight of a person who is 5 feet 1 inches tall. Round to the nearest pound.