Unit 5: Exponents and Exponential Relations Unit Test : 1. Evaluate the following. Write answers as fractions where appropriate.

a) (-2)

3 b) - 4

4 c) ( )3

65 d) 4

–3

e) 2 – (-3)2 f ) -(-7)

0 g) 1 – 3

-1 (answer as fraction)

2. Simplify the following expressions, writing answer as a single power.

a) )3)(3)(3( 54 b) )5)(5( 79− c) 3

5

)09.1(

)09.1(−

d) 3

12

5

5 e )

7)2(

)2(

−

− f ) 24 ])3[( −−

3. Complete the table of values shown below for the relation y = 1.8 x.

Round off answers to two decimal places.

x y -2 -1 0 1 2

4. Identify which of the following exponential relations would have a

STEEPER curve than y = 1.8 x and explain your strategy.

Note: There may be more than one answer.

a) y = 1.5 x b) y = 2 x c) y = (4/3)x d) y = (19/10) x

5. Identify which of the following relations would be decreasing and explain your strategy. Note: There may be more than one answer.

a) y = 1.1 x b) y = (1/2) x c) y = (0.9)x d) y = 7 x

6. The population of a small town is represented by the formula

P = 12500(0.98)

t where P is the number of people and t is time in years.

a) Is the town's population increasing or decreasing? Explain how you

know.

b) What is the initial population of the town?

c) In terms of percentage, how is the town’s population changing each year?

d) Determine the population of the town 10 years from now. Round

answer to nearest whole person.

e) A town just down the road has the same initial population, and is

expected to grow by 5% each year. Write a general equation to represent this other town's population.

7. Determine the growth or decay factor for each of the following scenarios:

a) A newspaper carrier wants to double the number of his deliveries each week.

b) A long-distance runner wants to decrease his running time by 1% each month.

c) A girl on a trampoline bounces to a height that is 6/7 the height of the previous bounce.

d) The price of gas has risen about 25% every year in some areas.

8. A new website had 1125 hits in the first week. They expect to triple

the number of hits each week. How many hits will the website get in the fifth week? Show the formula you used to get your answer.

9. Bismuth-214 is an isotope with a half-life of approximately 20 minutes.

a) How many mg will remain from a 240 mg sample after 100 minutes? Show the formula you used to get your answer.

b) What percentage of a sample would remain after one hour? Answer to one decimal place.

10. For each relation, state whether it is linear, quadratic, or exponential and

provide a reason for your choice

a) y = 1.07x

2 b) y = 500(2.5)x

c) d) 11. For each table below, use first and/or second differences to determine

whether the relation is linear, quadratic or exponential. If exponential, calculate the common ratio as well.

a)

b)

complete if

necessary complete if necessary

x

y First

Differences Second

Differences

Common Ratio

-3 -7 -2 -2.5 -1 2 0 6.5 1 11

complete if

necessary complete if necessary

x

y First

Differences Second

Differences

Common Ratio

-1 0.75 0 3 1 12 2 48 3 192

−1 1 2 3 4 5 6

−3

−2

−1

1

2

3

4

y

x

−1 1 2 3 4 5 6

−3

−2

−1

1

2

3

4

y

x

12. a) What happens when you attempt to evaluate 0

-1 on your

calculator?

b) What does that tell you about the value of 0

-1?

c) Use your knowledge of negative exponents to explain why your

calculator did what it did when trying to evaluate this power.

13. Rewrite 35

1−

as a power with a positive exponent.

14. Explain why y = 1

x is not an exponential relation.