8th Grade Math Final Exam Review Name: ___________________

Find the initial value and growth factor for each of the situation below then plug them in to y = a(b)x to get the function

that models the problem.

1. You deposit $200 into a bank account. Every year that account increases by 12 %. [EXAMPLE]

Initial value: 200

Growth factor: 1.12

Equation: y=200(1.12)x

2. The population of an apartment building is 4,000 people. Every month the population goes down by 12%.

Initial value:

Growth factor:

Equation:

3. You start a bank account with $500 and the interest on the account is 8% every year.

Initial value:

Growth factor:

Equation:

4. The New York Mets sign a new player for $8,000,000 and his salary goes up by 3% every year.

Initial value:

Growth factor:

Equation:

5. A certain stock was worth $42 at the beginning of the day. Every hour the stock goes down by 15%.

Initial value:

Growth factor:

Equation:

After coming up with an equation that models the situation we can find values in the future by plugging in values for x.

For example, in problem one you can find the amount of money in your bank account after 4 years by plugging in 4 for x.

y = 200(1.12)(4) = $314.70

Try finding the answers to the following questions by plugging in to the equations you found in problems 1-6.

1b) How much money do you have in your bank account after 5 years?

2b) How many people live in the building after 3 months?

3b) How much do you have in your bank account after 4 years?

4b) How much does the player make after 3 years?

5b) How much is the stock worth after 7 hours?

6. The half-life of Strontium-90 is 25 years. Every 25 years, fifty percent of the substance degrades and

only half the amount is left.

How many years will it take for a 40 mg sample to decay to 1.25 mg? ____________

Make a table to model this problem. Write an equation to model this problem.

7. The half-life of a sodium isotope is 15 hours. Every 15 hours, fifty percent of the substance degrades

and only half the amount is left.

How many hours will it take for a 120 mg sample to decay to 1.875 mg? ____________

Make a table to model this problem. Write an equation to model this problem.

8. The half-life of iodine-124 is 4 days. Every 4 days, fifty percent of the substance degrades and only half

the amount is left.

How many days will it take for a 80-mCi sample to decay to 2.5 mg? ____________

Make a table to model this problem. Write an equation to model this problem.

x y

2010 1000

2011 3000

2012 9000

2013 27,000

2014 81,000

Linear or exponential? _______________ Linear or exponential? _______________

y = _______________ y = ________________

x y

-1 1

0 4

1 16

2 64

3 256

Linear or exponential? _______________ Linear or exponential? _______________

y = _______________ y = ________________

Use an area model to simplify each expression.

x y

2010 1000

2011 2000

2012 4000

2013 8000

2014 16,000

x y

-1 -4

0 1

1 6

2 11

3 16

Use an area model to simplify each expression.

Write an expression for the volume of each shape.

4x3

X2

5x2

x

2x4

3x3

3x3

3x3

The solution of this equation has an error. Identify at which step the error occurred. _____

5x + 2 – 2x = 9 + 7

Step 1: 5x + 2 – 2x = 16

Step 2: 7x + 2 = 16

Step 3: 7x = 14

Step 4: x = 2

A. Step 1 B. Step 2 C. Step 3 D. Step 4

The solution of this equation has an error. Identify at which step the error occurred. _____

2(x + 4) + 6 = 14

Step 1: 2x + 4 + 6 = 14

Step 2: 2x + 10 = 14

Step 3: 2x = 4

Step 4 x = 2

A. Step 1 B. Step 2 C. Step 3 D. Step 4

A student worked the following problem: Solve: 8x + 10 – 6x + 4 = 24

Their work is shown below:

Step 1 2x + 14 = 24

Step 2 2x = 38

Step 3 x = 19

Which statement is correct? _____

A. There is an error in Step 1

B. There is an error in Step 2

C. There is an error in Step 3

D. No errors were made. The problem was worked correctly.

A firm has weekly fixed costs associated with the manufacture of dresses and a cost per dress

to produce. The firm then sells all the dresses it produces. The profit equation is:

P = 75x – (25x + 80,000)

a. How much does it cost to produce each dress? __________

b. What is the profit from selling 100 dresses?

c. How many dresses does the firm need to sell to make a profit of $2500?

d. What is the break-even point?

Dakota’s junior class decided to throw a dance to raise money for their class field trip. The

paid for a DJ, refreshments and wrist bands to be used as tickets. The profit equation is:

P = 5x – (2.50x + 75 + 175)

a. How much is it to get into the dance? __________

b. What is their profit if 200 students show up?

c. They would like to raise $3,000, how many students will they need to show up?

Movies Are Us has two video rental plans. The Regular video rental plan charges $ 3.25 for

each video rental. The Preferred video rental plan has an $ 8.75 membership fee and charges $

2 for each video rental.

a. Write a system of equations to model this scenario.

b. How many video rentals give the two plans the same cost?

c. Which video plan costs more for 18 video rentals?

d. Which plan provides more videos for $ 30.00?

Jonas needs a cell phone. He has a choice between two companies with the following monthly

billing policies. Each company’s monthly billing policy has an initial operating fee and charge

per minute. Terri’s Telephone has an operating fee of $29.95 and charges $0.14 per minute.

Carrie’s Connection has an operating fee of $4.95 and charges $0.39 per minute.

a. Write a system of equations to model this scenario.

b. At how many minutes is the monthly cost the same?

c. Which plan costs more 150 minutes of calls each month?

d. Which plan provides more minutes for $ 60.00?

There are 24 questions on a test. Each question is worth either 4 points or 5 points. In total

the test is worth 100 points.

a. Write a system of equations to model this situation.

b. How many 4-point questions are on the test?

c. How many 5-point questions are on the test?

Solve these systems of equations.

1. y = 4x + 3 2. y = -2x + 2

y = -x – 2 y = -2x – 2

3. y = 5

3𝑥 + 3 4. y = 3x – 4

y = 1

3𝑥 − 3 y =

−1

2𝑥 + 3

State whether the table, graph, or word problem is Linear, exponential, or inverse under the correct column. Please

EXPLAIN your answer

Problem Linear, Exponential, or inverse (Why?) 1.

X Y

1 24

2 12

3 8

4 6

10 2.4

2. X Y

0 15

1 20

2 25

3 30

4 35

3. X Y

0 3

1 9

2 27

3 81

4 243

4. Mr. Vitale’s IQ is 240. He is so smart that it doubles every day. What would his IQ be at the end of the week?

5. Ms. Wegryn and Ms. Matt take a trip to the lake. Every hour, they catch a total of 5 fish. How much fish will they have caught in 4 hours?

6. If x varies inversely with y, how does the graph look with when it has a constant of 72?

7.

8.

9.