Unit 5 Review

Vocabulary

100

What does a represent in y=ab^x

Initial Value

200

The set of all possible output values (y-values) is what?

The Range

300

What is the numerical factor of a term containing a variable (e.g., 3 in 3x)

Coefficient

400

What does zeros mean?

The x- values where f(x) = 0 

(Aka the roots)

500

This is an invisible line that the graph approaches, but never touches or crosses. It affects exponential graphs.

Asymptote

Exponential Functions

100

What is the formula for exponential growth? 

y = a(1+r)^x

200

Which one is an exponential function

Function A) 

x:0,1,2 ,3 

y:2,4,6,8

Function B)

x:0,1,2,3

y:3,9,27,81 

Function B

300

Write the exponential function using the real world problem below.

Sophia buys a motorcycle for 600 dollars and the price depreciates by 50% after one year.

600(.5) = 300

400

Is this exponential growth or decay?

What is the percent growth/decay rate?

y=12(0.7)^x

Decay.  30%

500

Annual sales of a fast food restaurant are $450,958.87 and increasing at a rate of 7%. What will the annual sales be in 6 years?

450,874(1.07)6 =$676,767.66

Monomials

100

Subtract -4ab² from -10ab²

-6ab²

200

(1/4)(8mn)(-6m²n²)

-12m³n³

300

(3x)² * (1/2)^-3

72x²

400

Simplify. Answer must contain positive exponents only.

-9x⁸y³ ⋅ 4x^-2y¹¹ + 7x⁶y¹⁴

-29 x⁶ y¹⁴

500

2 x⁴y³z⁵ - ¼ * x²yz⁵ * (xy)²

1¾ x⁴y³z⁵

Exponent Rules

100

Write out the product rule

x^a*x^b = x^a+b

200

Write out the quotient rule

x^a/x^b = x^a-b

300

Write out the Power Rule

(x^a)^b= x^a*b

400

Write out the Zero Exponent Rule

x⁰=1

500

Write out the Negative Exponent Rule

x^-a= 1/x^a

Exponential Functions - 2

100

Determine if the function shows exponential growth or decay?

y=3(.67)^x

Exponential decay

200

f(x)=a(1.07)x

Does this functions represent exponential growth or decay? What's the percent growth/decay factor?

Exponential Growth.  7%.

300

Does the graph represent exponential growth or decay?

Exponential Growth

400

2243

500

Ms. Wiggins purchased a car for 26,400 and every year it decays by 12%. What can she expect the value of her car to be after 3.5 years?  

f(x)=26400(.88)3.5=$16,876.92