Exam 1: Functions and Change

The bill for electricity is $200 when 55 kilowatt hours are used and $300 when 95 kilowatt hours are used. A. The base cost (without using any electricity) is $______. B. Each additional kilowatt hour used costs $_____.

One of the following tables of data is linear and the other one is exponential. The formula for the exponential one is . Find the values of c and d to two decimal places. A. c=_____ B. d=_____

The number of species, S, on an island is proportional to the square root of the area, A, of the island. An island which has an area of 25 square miles contains 30 species. How many species would be expected on an island of 9 square miles?

A population is growing according to the formula , where P is the population in year t. How many years will it take for the population to exceed 1000?

Suppose that is the price per unit (in dollars) of widgets which will induce producers to supply q thousand widgets to the market, and suppose that is the price per unit at which consumers will buy q thousand units. Which is larger, S(150) or S(100)?

The following figure gives both supply and demand curves for a certain product. If the price is $50 per item, how many items will the consumers buy?

What is the equation for the graph obtained by shifting the graph of vertically upward by 2 units, followed by vertically stretching the graph by a factor of 5, followed by reflecting the graph across the x-axis?

A bar of soap starts out at 100 grams. Write a formula for the quantity S grams of soap remaining after t days if the decrease is 5% per day

Joe invested $10,000 in the stock market, while Sam invested $20,000. Joe's investment increased by 6% per year for 10 years. Sam's investment decreased in value by 12% per year for 5 years and then increased by 12% per year for the next 5 years. What was Joe's investment worth after 10 years? Round to the nearest dollar.

The graph of is shown in the following figure. Is the graph concave down or concave up at x = 4?

The following table gives values of three functions. Which one(s) could possibly be linear? Select all that apply.

Give a possible formula for the function shown in the following table.

Let and . What is ?

Solve for t. Round to 3 decimal places.

The number of reported offenses of violent crime in the U.S. between 1983 and 1996 is given in the following table. A. Find the average rate of change between 1983 and 1992 (to the nearest integer). B. Find the average rate of change between 1992 and 1996 (to the nearest integer).

Production costs for manufacturing T-shirts consist of a fixed cost of $18,000 plus variable costs of $2 per shirt. Each T-shirt sells for $8 dollars. How many T-shirts must be sold for the company to break even?

From the following table, A. Find f(4) B. Find the value(s) of x for which . If there is more than one, list them in increasing order, separated by commas.

At high tide, the water level is 6 feet below a certain pier. At low tide, the water level is 18 feet below the pier. Assuming sinusoidal behavior, let = the water level relative to the pier, at time t (in hours). At t = 0 the water is -12 feet and falling until it reaches the first low tide at t = 3. Give a formula for .

Write the function in the form . Round k to 3 decimal places.

A population of rabbits is growing. In 2005, there were 10,000,000 rabbits, and the population was increasing at a rate of 20% per decade. What is the predicted rabbit population in 2016? Round to the nearest rabbit.