Exam 4: Exponential Functions

Which of the following is correctly ordered from least to greatest?

For an account paying 9% annual interest, compounded continuously, the nominal rate is _____ % and the effective rate is _____ %. Round to 3 decimal places.

A population is 150,000 in year t = 0 and declines at a continuous rate of 2% per year. By what percentage does the population decrease each year? Round to 2 decimal places.

An investment decreases by 20% over a decade. By what effective annual rate does it decrease? Give your answer correct to four decimal places.

The table below shows v, the dollar value of a share of a certain stock, as a function of t, the time (in weeks) since the initial offering of the stock. A possible formula for is . Round the second answer to 3 decimal places.

The US population in 2005 was approximately 296.4 million. Assume the population increases at a rate of 1.22% per year. Some demographers believe that the ideal population of the United States is about 130 million. According to this model, in what year did this occur?

Let be the intersection of the graphs of the two exponential functions and , where . If s is decreased, does increase, decrease, or stay the same?

The population of a city has been growing at a rate of 6% per year. If the population was 140,000 in 1990, what was the population in 1995? Round to the nearest whole number.

A radioactive substance decays by 11% every year. Which of the following is the formula for the quantity, , of a 20 gram sample remaining after years?

Without a calculator, graph the following on the same set of axes: A) B) C)

In 2006, the cost of a particular piece of computer equipment was $500 and going down at a rate of 10% per year. Assuming this percentage remains constant, what is the formula for C, the cost of this equipment in dollars, as a function of t, the number of years since 2006?

Suppose the amount of ozone in the atmosphere is decreasing exponentially at a continuous rate of 0.26% per year. How many years will it take before one-fourth of the ozone has disappeared? Round to the nearest year.

Kevin buys a new CD player for $190, and finds two years later when he wants to sell it that it is only worth $45. Assuming the value of the CD player decreases exponentially, the formula for , the value of the CD player after t years, is given by . Round your second answer to 2 decimal places.

If you start with $4000, how much money will you have after a 25% increase?

Each of the functions in the table below is increasing, but each increases in a different way. One is linear, one is exponential, and one is neither. Which one is linear: f, g, or h?

Write a formula that gives the value in an account after t years. Assume that the initial value in the account is $1200 and that the account doubles in value every 8 years.

Which bank has the best effective annual yield?

Is the formula for a function representing a quantity which begins at N in year t = 0 and grows at a continuous annual rate of % given by ?

Suppose you would like to have $20,000 in 10 years. What is the minimum amount you need to deposit into a bank account earning 3% compounded weekly to reach this goal?

Let give the size of a population of animals in year t. After how many years will the population be approximately 770?