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Worksheet – 4.1-4.2 NAME______________________________

*Algebra Review of exponents x m x a x b x a*

* b b x*

* h b x b h x m*

* n x n*

1

* x*

*1 x*

*If b x b y x*

* then x*

* y*

* x a x*

1

2 x b

*3 simplified x*

*1 x*

*3 b*

0

*1 if b n*

* n x mn x m*

*0 x m n*

Simplify the following. Express your final answer with positive exponents.

*25 p*

8

1.

*10 p*

*4 q*

2. 4 z

4

*2 z*

*3. a*

*4 b*

*5 b*

2 a 7

1

1

* y y*

5

3

4.

* x*

3

*5 x y*

4

2

3

*5. a*

1

1

* b*

1

Solve for x :

*6. x*

*2 e*

x

*5 xe*

x

0

Solve for t without using logarithms:

5

* t*

1

7.

2

*3 t*

4

*8. Write a possible exponential function in the form y*

*Cb x*

*, with b*

*0 , b*

1 .

b) (0, 5) and (3, 10) c) (-2, 64) and (2, 20.25)

9. If $10,000 is invested at an interest rate of 3% per year, compounded semiannually, find the value of

the investment if it was invested for 4 years.

10. If $10,000 is invested at an interest rate of 3% per year, compounded continuously, find the value of the investment if it was invested for 7 years.