Name:    AII.9 - Curve of Best Fit

Multiple Choice
Identify the choice that best completes the statement or answers the question.

1

The amount of lost revenue from tickets not sold for a concert is shown in the table.  The ticket prices include tax.

Lost Revenue From Tickets Not Sold
 Price per Ticket (x) \$25 \$35 \$55 \$125 Number of Tickets Not Sold 84 80 92 323 Amount of Lost Revenue (y) \$2,100 \$2,800 \$5,060 \$40,325

Which equation best models the relationship between y, the amount of lost revenue, and x, price per ticket?
 a. c. b. d.

2

Which of the following equations best models the data in this table?

 a. b. c. d.

3

Which equation best represents the data in this table?

 a. c. b. d.

4

The population of a state is counted every ten years.  In the table,       populations are given for every twenty years.  At the rate the state is growing, what would be the best estimate for the population in the year 2020?
 Year population (to nearest 1000) 1800 478,000 1820 639,000 1840 753,000 1860 993,000 1880 1,400,000 1900 1,894,000 1920 2,559,000 1940 3,572,000 1960 4,556,000 1980 5,880,000 2000 8,049,000
 a. 6,970,000 c. 16,000,000 b. 10,600,000 d. 100,600,000

5

At 1,821 feet tall, the CN Tower in Toronto, Ontario, is the world’s tallest self-supporting structure.  A penny is dropped from the observation deck on top of the tower and falls to the ground.  The table shows the penny’s distance from the ground after various periods of time (in seconds) have passed.  Where is the penny located after falling for a total of 10.5 seconds?
 Time (seconds) Distance (feet) 0 1821 2 1757 4 1565 6 1245 8 797 10 221
 a. 57 feet b. 140 feet c. 221 feet d. 300 feet

6

Mike deposited \$1000 in an account.  Over 5 years the account has grown exponentially as shown in the table.  Assuming the rate of growth continues to be the same, predict the amount of money Mike will have after 10 years.

 Years (t) 0 1 2 3 4 5 Money A(t) \$1000 \$1061.80 \$1127.50 \$1197.20 \$1271.20 \$1349.90
 a. \$1716.00 b. \$1822.20 c. \$2699.80 d. \$5000.00

Numeric Response

7

The table provides the value of an account over time that earned annual compound interest.  There was an initial deposit of \$1,500 into the account and no other deposits were made.

Value of Account Over Time
 Time in years, x 0 5 10 15 20 25 30 Value in dollars 1,500.00 1,914.42 2,443.34 3,118.39 3,979.95 5,079.53 6,482.91

Assuming the account continues to grow in the same way, use the exponential curve of best fit to find the value of the account at the end of 40 years, rounded to the nearest dollar.