7 Chapter Review

Connecting BIG ideas and Answering the Essential Questions

1 Equivalence One way to represent numbers is in scientific notation. This form uses powers of ten to write very large or very small numbers.	Zero and Negative Exponents (Lesson 7-1) 10 0 = 1 10 to the , equals 1 10 − 3 = 1 10 3 10 super negative 3 end super , equals , fraction 1 , over 10 cubed end fraction	Scientific Notation (Lesson 7-2) 175 , 000 , 000 , 000 , 000 = 1.75 × 10 14 0.0000568 = 5.68 × 10 − 5 table with 2 rows and 1 column , row1 column 1 , 175 comma 000 comma 000 comma 000 comma 000 equals , 1.75 , times , 10 to the fourteenth , row2 column 1 , 0.0000568 . equals , 5.68 , times , 10 super negative 5 end super , end table
2 Properties Just as there are properties that describe how to rewrite expressions involving addition and multiplication, there are properties that describe how to rewrite and simplify exponential expressions.	Properties of Exponents (Lessons 7-3, 7-4, and 7-5) 5 2 · 5 4 = 5 2   + 4 = 5 6 ( 3 7 ) 4 = 3 7   · 4 = 3 28 ( 6 x ) 4 = 6 4 x 4 7 8 7 5 = 7 8 − 5 = 7 3 ( y 2 ) 5 = y 5 2 5 table with 4 rows and 1 column , row1 column 1 , 5 squared , middle dot , 5 to the fourth , equals , 5 squared . super plus 4 end super , equals , 5 to the sixth , row2 column 1 , open , 3 to the seventh , close to the fourth . equals , 3 to the seventh . super middle dot 4 end super , equals , 3 to the twenty eighth , row3 column 1 , open , 6 x , close to the fourth . equals , 6 to the fourth , x to the fourth , row4 column 1 , table with 2 rows and 1 column , row1 column 1 , fraction 7 to the eighth , over 7 to the fifth end fraction . equals . 7 super 8 minus 5 end super . equals , 7 cubed , row2 column 1 , open , y over 2 , close to the fifth . equals . fraction y to the fifth , over 2 to the fifth end fraction , end table , end table
3 Function The family of exponential functions has equations of the form y = a · b x . y equals eh middle dot , b to the x , .  They can be used to model exponential growth or decay.	Exponential Functions (Lesson 7-6) Image Long Description	Exponential Growth and Decay (Lesson 7-7) Exponential growth is modeled by the function y = a · b x , y equals eh middle dot , b to the x , comma  where a > 0 eh greater than 0  and b > 1 . b greater than 1 .  Exponential decay is modeled by the function y = a · b x , y equals eh middle dot , b to the x , comma  where a > 0 eh greater than 0  and 0 < b < 1 . 0 less than b less than 1 .

Chapter Vocabulary

• compound interest (p. 456)
• decay factor (p. 457)
• exponential decay (p. 457)
• exponential function (p. 447)
• exponential growth (p. 455)
• growth factor (p. 455)
• scientific notation (p. 420)

Choose the correct term to complete each sentence.

1. ? is a shorthand way to write very large and very small numbers.
2. For a function y = a · b x , y equals eh middle dot , b to the x , comma  where a > 0 eh greater than 0  and b > 1 , b greater than 1 comma  b is the ?.
3. For a function y = a · b x , y equals eh middle dot , b to the x , comma  where a > 0 eh greater than 0  and 0 < b < 1 , b 0 less than b less than 1 comma b  is the ?.
4. The function y = a · b x y equals eh middle dot , b to the x  models ? for a > 0 eh greater than 0  and b > 1 . b greater than 1 .
5. The function y = a · b x y equals eh middle dot , b to the x  models ? for a > 0 eh greater than 0  and 0 < b < 1 . 0 less than b less than 1 .

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