Lesson 6.1-6.2 Review Alg 2

Solving Exponential Equations (common base)

100

Solve for x

9^3x-7=9^5-x

x=3

200

8^6y+4=64

x=-1/3

300

(1/27)=3^4n-1

n= -1/2

400

4ⁿ * 4^2n-9=64

n=4

500

2^3k-1*2^5k-7=16

k=3/2

Solving Exponential Equations (no common base)

100

What are the basic techniques for solving exponential equations?

Fill in the Blank

1.)Find a ____________ _________

2.) Use the Properties of ___________ to condense your equation

3.) Set the _________ equal and solve for the variable using inverse operations.

1.) Common Base

2.) Exponents

3.) Exponents 

200

3^x+2 = 1/9

x = -4

300

Solve the exponential equation: 3^(2x) = 27.

x=3/2

400

27³ⁿ=81²ⁿ⁺¹

n=4

500

36^n-3 * 216ⁿ=216²ⁿ⁺¹

n=-9

Exponential Growth and Decay

100

Fill in the Blank

1.) Exponential _______ is a concept in which a quantity increases at an accelerating rate proportional to its current value.

Growth

200

In 2002, there were 972 students enrolled at Kees' High School. Since then, the number of students has increased by 1.5% each year. How many students were enrolled in 2014?

1,162 students

300

An investment of $12,000 is losing value at a rate of 4% each year. Find the value of the investment after 9 years. 

$8,310.41

400

Using the function f(t)=35,000(0.92)^t 

1.) Is this function demonstrating growth or decay? 

2.) At what percent is this function increasing/decreasing? 

MUST GET BOTH

1.) Decay

2.) 8%

500

SJ moved $25,000 of his savings to a new investment account that earns 4.5% interest compounded monthly. Find the total amount in the account after 6 years if he does not withdrawal any money.

$32,732.58

Random Trivia

100

What gas do plants absorb during photosynthesis? 

Carbon Dioxide 

200

Which figure of speech compares using "like" or "as" ?

Simile 

300

In which year did World War II End?

1945

400

Which NBA team's mascot is a dinosaur? 

The Toronto Raptors

500

What year was the first iPhone released?

2007

Find Domain and Range

100

Graph on your graphing calculator and then state the the Domain and Range of f(x)=5^x 

**Must get both

Domain: (−∞,∞)

Range: (0,∞)

200

Graph on your graphing calculator and then state the the Domain and Range of f(x)=6^x-5 

**Must get both

Domain: (−∞,∞)

Range: (−5,∞)

300

Using f(x)=-2^x +1, state the horizontal asymptote 

y=1

400

Write an equation with a parent function of y=3^x that is reflected across the x-axis, shifted 4 units down and 2 units to the right.

**Must be 100% correct

y=-3^x-2 -4

500

Using f(x)=-2^x+5 

Name the parent function ______

List the transformations applied _____________ __________ 

State the domain and range of the function 

**Must get all parts for credit! 

Parent Function: y=2^x

Transformations: Reflection across x-axis, shift up 5 units 

Domain: (−∞,∞)

Range: (−∞,5)