Teacher resources and professional development across the curriculum

Teacher professional development and classroom resources across the curriculum

 Lesson Plans: Introduction Lesson Plan 1: Overrun by Skeeters - Exponential Growth Lesson Plan 2: Bigger and Smaller - Exponent Rules

Lesson Plan 1: Overrun by Skeeters - Exponential Growth

The questions below dealing with exponential functions have been selected from various state and national assessments. Although the lesson above may not fully equip students to answer all such test questions successfully, students who participate in active lessons like this one will eventually develop the conceptual understanding needed to succeed on these and other state assessment questions.

• Taken from the Massachusetts Comprehensive Assessment, Grade 10 (Spring 2002):

The number of bacteria in a culture doubles each hour. Which graph below best represents this situation?

• Taken from the Maine Education Assessment, Grade 11 (March 2002):

 Country 1997 Population (in millions) Estimated 2002 Population (in millions) China 1221.6 1272.3 India 967.6 1042.3 United States 268.0 279.5 Indonesia 209.8 225.6

This table shows the 1997 and estimated 2002 populations of the four most populous countries in the world. Jessica and Katy are using the data for a presentation of their world geography report.

1. Jessica says that between 1997 and 2002 the population of China increased faster than that of the United States. Katy insists that the United States population increased more quickly. Explain how each of them can be correct. Justify your answer mathematically.

2. Suppose the table was extended for additional five year periods (2007, 2012, 2017, etc.). If the population of the United States continues to grow at the percentage rate that is predicted in this table, after how many five year periods will the population reach 300 million? Show or explain how you found your answer.
Solution:
1. The population of China increased by 50.7 million, but the population of the United States only increased by 11.5 million; hence, Jessica stated that the population of China was increasing faster. On the other hand, the population of China increased by only 4.1 percent, while the population of the United States increased by 4.3 percent; consequently, Katy said that the population of the United States was increasing faster.

2. The population of the U.S. in 2007 will be 279.5 × 1.043 291.5 million. In 2012, the population will be 291.5 × 1.043 304.1 million. In 10 years, or after two more five year periods, the population will be over 300 million.

• Taken from the Maine Education Assessment, Grade 11 (March 2002):

Dave's Electronics is having a sale on radios. Each day the price of every radio will be reduced 5% from the previous day's price. If the price of a radio before the sale was \$50, which expression can be used to find its price on the nth day of the sale?
A. 50 - 0.05n
B. 50 - 50n(0.95n)
C. 50(0.05)n