7 Chapter Test

Do you know HOW?

Simplify each expression.

1. r 3 t − 7 t 5 fraction r cubed . t super negative 7 end super , over t to the fifth end fraction
2. ( a 3 5 m ) − 4 open . fraction eh cubed , over 5 m end fraction . close super negative 4 end super
3. c 3 v 9 c − 1 c 0 c cubed , v to the ninth . c super negative 1 end super . c to the
4. 2 y − 9 h 2 ( 2 y 0 h − 4 ) − 6 2 , y super negative 9 end super . h squared . open . 2 , y to the . h super negative 4 end super . close super negative 6 end super
5. ( 1.2 ) 5 ( 1.2 ) − 2 open 1.2 close to the fifth . open 1.2 close super negative 2 end super
6. ( − 3 q − 1 ) 3 q 2 open . negative 3 , q super negative 1 end super . close cubed . q squared

Write each number in scientific notation.

7. 79,500,000,000
8. 0.0000000405

Write each number in standard notation.

9. 8.4 × 10 − 6 8.4 times , 10 super negative 6 end super
10. 9.52 × 10 11 9.52 , times , 10 to the eleventh

Simplify each expression. Write each answer in scientific notation.

11. ( 6 × 10 4 ) ( 4.8 × 10 2 ) open 6 times , 10 to the fourth , close open 4.8 times , 10 squared , close
12. 1.5 × 10 7 5 × 10 − 2 fraction 1.5 times , 10 to the seventh , over 5 times , 10 super negative 2 end super end fraction

13. Medicine The human body normally produces about 2 × 10 6 2 times , 10 to the sixth  red blood cells per second.

    1. Use scientific notation to express how many red blood cells your body produces in one day.
    2. One pint of blood contains about 2.4 × 10 12 2.4 times , 10 to the twelfth  red blood cells. How many seconds will it take your body to replace the red blood cells lost by donating one pint of blood? How many days?

Evaluate each function for x = − 1 x equals negative 1 , 2, and 3.

14. y = 3 · 5 x y equals 3 middle dot , 5 to the x
15. f ( x ) = 1 2 · 4 x f open x close equals , 1 half , middle dot , 4 to the x
16. f ( x ) = 4 ( 0.95 ) x f , open x close , equals 4 . open , 0.95 , close to the x

Graph each function.

17. y = 1 2 · 2 x y equals , 1 half , middle dot , 2 to the x
18. y = 2 ⋅ ( 1 2 ) x y equals 2 dot . open , 1 half , close to the x
19. Banking A customer deposits $2000 in a savings account that pays 5.2% interest compounded quarterly. How much money will the customer have in the account after 2 yr? After 5 yr?

20. Automobiles Suppose a new car is worth $30,000. You can use the function y = 30 , 000 ( 0.85 ) x y equals 30 comma 000 . open , 0.85 , close to the x  to estimate the car's value after x years.

    1. What is the decay factor? What does it mean?
    2. Estimate the car's value after 1 yr.
    3. Estimate the car's value after 4 yr.

Do you UNDERSTAND?

21. Error Analysis Find and correct the error in the work shown below.

    

22. Open-Ended Write two equivalent expressions. Use a negative exponent in one of the expressions.
23. Writing Explain when a function in the form y = a · b x y equals eh middle dot , b to the x  models exponential growth and when it models exponential decay.
24. Simplify the expression ( a 6 a 4 ) 2 open . fraction eh to the sixth , over eh to the fourth end fraction . close squared  in two different ways. Justify each step.
25. Reasoning Explain how you can use the property for dividing powers with the same base to justify the definition of a zero exponent.

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