Exam 1: Functions and Change

For and , find and simplify .

Each of the curves in the following figure represents the balance in a bank account at time t after a single deposit at time t = 0. Assuming continuously compounded interest, which curve represents the smallest initial deposit?

The population of Nicaragua was 3.6 million in 1990 and growing at 3.4% per year. Let P be the population in millions, and let t be the time in years since 1990. Express P as a function of t. Select all that apply.

The population of Los Angeles, California was 2,811,801 in 1970 and was 3,448,613 in 1994. The average rate of change in the population of Los Angeles between 1970 and 1994 was _____ people per year.

Which of the following are power functions? Select all that apply.

Coulomb's law says that the electrical force between two charged objects is directly proportional to the product of the quantity of charge on the objects and inversely proportional to the square of the distance between the objects. Let and be the charge on the two objects. Let d be the distance between the objects and F be the electrical force between them. Translate Coulomb's Law into mathematical symbols.

Write an equation of a periodic function with amplitude 35, vertical shift 50, period , and horizontal translation (phase shift) 2 units to the right.

A standard cup of coffee contains about 100 mg of caffeine, and caffeine leaves the body at a rate of about 17% an hour. How many mg of caffeine are left in the body after 6 hours if this rate is continuous? Round to 2 decimal places.

An exponentially decaying substance was weighed every hour and the results are given below. If the formula gives the weight of the substance, Q, at time t in hours since 9 am, then =_____ and k=_____. Round k to 2 decimal points.

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

Find the equation of the line in the following figure.

Temperature in Town A oscillates daily between F at 4am and F at 4pm. If is a formula for the temperature in Town A in terms of time, where time is measured in hours from 4 am, then A =_____, B =_____, C =_____, and D =_____.

Use your calculator to find all of the solutions to the equation . Round your answers to 2 decimal places.

Find the value for b in the following table of values for the linear function f.

The total sales of household computers in the U.S., as measured by sales to retail consumer dealers, in millions of dollars, was 2,385 in 1984 and 16,585 in 1997. A. Find the average rate of change in sales between 1984 and 1997 (in millions of dollars, to the nearest tenth). B. Use your answer to estimate total sales in 2000 (in millions of dollars, to the nearest tenth).

The size of a bird population on an island can be described by a sinusoidal graph. The number of birds on the island decreased from a maximum of 20,000 in 1943 to a minimum of 12,000 in 1989, and then began increasing again. In what year will the population begin decreasing again?

A $3000 pump depreciates linearly . It is worth $2200 in 4 years. Find a formula for the value of the pump, V, as a function of time, t (in years) since it was purchased.

The following table gives values for three different functions. One of the functions is neither linear nor exponential. Is that function increasing or decreasing?

Give a formula for the following sinusoidal function as a transformation of .

The illumination, I, of a candle is inversely proportional to the square of its distance, d, from the object it illuminates. Write a formula that expresses this relationship.