Algebra II H/G Section-07-02 ALGEBRA II HONORS/GIFTED - SECTION 7-2 (Properties of Exponential Functions) 5/1/2019 Algebra II H/G Section-07-02 Properties of Exponential Functions

Transformations of Exponential Functions 1) Graph y = 𝟒 𝒙 using y-intercept: Domain: Range: Asymptote:

Transformations of Exponential Functions 2) Graph y = 𝟐 𝒙 and y= 3 ∙𝟐 𝒙 using Compare both graphs: y-intercept: Domain: Range: Asymptote:

Transformations of Exponential Functions 3) Graph y = 𝟐 𝒙 and y = 𝟏 𝟐 ∙𝟐 𝒙 using Compare both graphs: y-intercept: Domain: Range: Asymptote:

Transformations of Exponential Functions 4) Graph y = 𝟐 𝒙 and y = 𝟐 𝒙−𝟐 using Compare both graphs: y-intercept: Domain: Range: Asymptote:

Transformations of Exponential Functions 5) Graph y = 𝟐 𝒙 and y = 𝟐 𝒙 −𝟑 Compare both graphs: y-intercept: Domain: Range: Asymptote:

Transformations of Exponential Functions 6) Graph y = 𝟐 𝒙 and y =−𝟐 𝟐 𝒙+𝟐 +𝟒 Compare both graphs: y-intercept: Domain: Range: Asymptote:

base moves the graph up (+) or down (-) moves the graph left (+) or right (-) moves the graph up (+) or down (-) shrinks or stretches base

Natural Base Exponential functions Exponential functions with base e 7) Graph y = 𝒆 𝒙 and evaluate 𝒆 𝟒 to four decimal places

Continuous Compounded Interest Formula A(t)=P 𝒆 𝒓𝒕 Amount in account at time t Interest rate (annual) principal time in years

8) Chloe deposited $2500 in an account that pays 6% annual interest compounded continuously. How much will he have in her account after 5 years? $3374.65

9) Emilia is researching a newly- discovered species of bacteria 9) Emilia is researching a newly- discovered species of bacteria. At time t = 0 hours, she puts one hundred bacteria into what she has determined to be a favorable growth medium. The bacteria are growing at a rate of 25%. Assuming continuous growth, what is the population of the bacteria after six hours? About 448 bacteria.