7 Pull It All Together

BIG idea Equivalence

One way to represent numbers is in scientific notation. This form uses powers of ten to write very large or very small numbers.

Task 1

Medical X-rays, with a wavelength of about 10 − 10 10 super negative 10 end super  m, can penetrate completely through your skin.

1. Ultraviolet rays, which cause sun burn by penetrating only the top level of skin, have a wavelength about 1000 times the wavelength of an X-ray. Find the wavelength of ultraviolet rays. Show your work.
2. The wavelengths of visible light are between 3.8 × 10 − 7 3.8 times , 10 super negative 7 end super  m and 7.6 × 10 − 7 7.6 times , 10 super negative 7 end super  m. Are these wavelengths longer or shorter than those of ultraviolet rays? Explain.

BIG idea 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.

Task 2

Write each answer as a power of 2. Show your work and explain your steps.

1. Computer capacity is often measured in bits and bytes. A bit is the smallest unit, which is a 1 or 0, in the computer's memory. A byte is 2 3 2 cubed  bits. A megabyte (MB) is 2 20 2 to the twentieth  bytes. How many bits are in a megabyte?
2. A gigabyte (GB) is 2 30 2 to the thirtieth  bytes. How many megabytes are in a gigabyte? How many bits are in a gigabyte?

BIG idea Functions

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.

Task 3

On January 1, 2010, Chessville has a population of 50,000 people. Chessville then enters a period of population growth. Its population increases 7% each year. On the same day, Checkersville has a population of 70,000 people. Checkersville starts to experience a population decline. Its population decreases 4% each year. During what year will the population of Chessville first exceed that of Checkersville? Show all of your work and explain your steps.

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