Chapter 7 Review

Exponents

100

Simplify with no negative exponents:

3^-2

1/9

200

Simplify with no negative exponents:

m^-4

1/m⁴

300

8^1/3

2

400

16^3/4

8

500

125^4/3

625

Writing a Linear Equation

100

Slope of - 2, Y- Intercept (0,3)

y = -2x + 3

200

Slope of 0.4, Y-intercept of (0,-3.5)

y = 0.4x - 3.5

300

A line that passes through the points (-5,4) and (3,-2)

y = -3/4x + 1/4

400

A line that passes through (7,16) and (2, -4)

y = 4x - 12

500

A line that passes through (2, 3) and (5, -6)

y = -3x +9

Writing an Exponential Equation

100

Y - Intercept: (0, 7)  Multiplier: 2

y=7(2)^x

200

Y- Intercept: (0,100)   Multiplier: 0.5

y = 100(0.5)^x

300

A savings account, with compound interest, starts with $2,000 and grows 5% every year. 

y=2000(1.05)^x

400

The value of a car with an initial purchase price of $12,000 depreciates by 11% per year. 

y = 12000(0.89)^x

500

The population in year 2000 was 281.4 million people. The population grew about 2% each year. 

(x is number of years) (y is people in millions)

y = 281.4(1.02)^x

Solving Systems

100

y = 3x + 11

y = - x +3 

(-2 , 5)

200

y = 2x + 3

y = 4 + x

(1, 5)

300

x + 2y = 16

x + y = 2

(-12, 14)

400

2x + 3y = 10

3x - 4y = -2

(2, 2)

500

-4x + 6y = -20 

2x - 3y  = 10

Infinite Solutions

Sequences

100

Write an explicit equation for the sequence:

1, 5, 9, 13, 17....  

t(n) = 4n - 3

200

Write an explicit equation for the sequence: 

-20, -30, -40, -50, -60...

t(n)=-10n - 10

300

Write an explicit equation for the sequence: 

3, 6, 12, 24, 48

t(n)=1.5(2)ⁿ

400

Write an explicit equation for the sequence: 

4, 20, 100, 500, 2500... 

t(n) = 0.8(5)ⁿ

500

Write a recursive equation for the sequence:

5, 12, 19, 26, 33 ... 

t(1)=5

t(n+1) = t(n) + 7