Exponential Function

Notes Day 8.1 PAP Algebra 2Objective: TLW…identify and sketch graphs of exponential functionsanalyze a situation modeled by an exponential function, formulate an equation, and solve the problemsolve exponential equations

Exponential Function a≠0, b>0,b≠1, xєR NOTES DAY 8.1 Exponential Growth Exponential Decay (0,a) (0,a) growthfactor decay factor b > 1, b = _______________ a = __________________ H. Asymptote: y = ______ 0 < b < 1, b = _______________ a = _________________ H. Asymptote : y = ______ y-intercept on parent fcn y-intercept on parent fcn 0 0

Exponential Growth Function : y=abxWhere a≠0b>1 ·3 +1 ·3 +1 ·3 +1 The “b” is NOT the y-intercept in an exponential function “a” is the starting point and b is the product from one y-value to the next Y = 2· 3x

Exponential Decay Function: y=abx Where a≠00<b<1 ·1/5 +1 ·1/5 +1 · 1/5 +1 The “a” is the starting point and soa = 5 The b is the product, so b = 1/5 y = 5· (1/5)x

Exponential Parent Function Shifts Vertical Stretch Causes a _________________ in the graph Vertical Shrink Causes a _________________ in the graph Reflection Causes a _____________ in the x-axis “h” causes a _______________________ in the graph Horizontal Translation “k” causes a _______________________ in the graph Vertical Translation

Exponential Growth Model Y = a(1+r)t The decay model is the same except the decay factor is 1 – r a = initial amount r = growth rate t = time period 1+r = growth factor So if the rate is 3% , then 1.03 is the growth factor

Growth Model real life example • You put $350 in a savings account that earns 3% annual interest compounded yearly. How much will that investment be worth in 4 years? Y = a(1+r)t Y = 350(1+0.03)4 Y ≈ $393.93 in 4 years

Graph y = 3(2)x (-∞,∞) (0,∞) (0,3) Complete a t-chart Domain: Range: Y-intercept:

Graph y=2(½)x+1 (-∞,∞) (1,∞) Y=1 Complete a t-chart Domain: Range: H. Asymptote:

What exponential function represents a situation where the population triples every year and starts with 2400. Equation:

Solve the equation for x: X=7

Solve the following equations • 1. 2. 3x = 27 3. 32X-1=27 X+2

Activity: Now lets see what you know. I will show you some problems. When I ask for the answer, please show the color of the matching correct answer. HW : WS 8.1 – which is is due next class. We will also be taking a quiz next class on these concepts.

Which line is the horizontalasymptote of the graph of y=2x • A. x = 0 • B. y = 0 • C. x = 2 • D. y = 2

The graph of y=3x is translated 1 unit up and 3 units to the right. Which of the following represents this function? • A. Y = 3x+1 + 3 • B. Y = 3x-1 + 3 • C. Y = 3x+3 + 1 • D. y = 3x-3 +1

The graph of y=3x is translated 1 unit left and 3 units up. Which of the following represents this function? • A. Y = 3x+1 + 3 • B. Y = 3x-1 + 3 • C. Y = 3x+3 + 1 • D. y = 3x-3 + 1

How is the graph of f(x) = 2x transformed to create the graph of f(x) =(-)2x? A. Translated up 1 unit B. Translated down 1 unit C. Reflected over the x-axis D. Reflected over the y-axis

A graph grows exponentially with a base of 3 and has a y-intercept of 2. Which of the following equations represents this? A. y=2(3)x B. y=3(2)x C. Y=2x3 D. y=3x2

A baseball card bought for $50 increases 3% in value each year. Write an exponential function which models how to find the value of the card after 5 years. Round to the nearest 100th. A. y=50(3)5 B. y=50(1.03)5 C. Y=3(50)5 D. y=1.03(50)5

What is the best first step to solve the equation 32x+2=81 for x • A. 2x+2=81/3 • B. 32x+2 =34 • C. 9x+2 = 81 • D. 32x+2 = 92

What is the best first step to solve the equation 3X = 9X-4 for x • A. X = X-4 • B. 3x =3-2X+8 • C. 3x = (32)X-4 • D. X = 2X-4

What is the best first step to solve the equation 4X-5 = 1/64 for x • A. X-5 = 1 • B. 4x-5 = 43 • C. 4x-5 = 4-3 • D. X-5 = 64

Your quiz next class will be on matching an exponential equation to its graph. Remember the shift rules you used in the practice problems we just covered – but you may also complete a t-chart to test numbers.

Exponential Function