Notes Day 8.1   PAP Algebra 2
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Notes Day 8.1 PAP Algebra 2 Objective: TLW… identify and sketch graphs of exponential functions analyze a situation modeled by an exponential function, formulate an equation, and solve the problem solve exponential equations. Exponential Function. a≠0, b>0,b≠1, x є R. NOTES DAY 8.1.

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Exponential Function

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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

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 a b x where a 0 b 1

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 a b x

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

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

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

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

Graph y = 3(2)x

(-∞,∞)

(0,∞)

(0,3)

Complete a t-chart

Domain:

Range:

Y-intercept:


Graph y 2 x 1

Graph y=2(½)x+1

(-∞,∞)

(1,∞)

Y=1

Complete a t-chart

Domain:

Range:

H. Asymptote:


Exponential function

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

Equation:


Solve the equation for x

Solve the equation for x:

X=7


Solve the following equations

Solve the following equations

  • 1. 2. 3x = 27 3. 32X-1=27 X+2


Exponential function

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 horizontal asymptote of the graph of y 2 x

Which line is the horizontalasymptote of the graph of y=2x

  • A. x = 0

  • B. y = 0

  • C. x = 2

  • D. y = 2


Exponential function

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


Exponential function

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 2 x transformed to create the graph of f x 2 x

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


Exponential function

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


Exponential function

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 3 2x 2 81 for x

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 3 x 9 x 4 for x

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 4 x 5 1 64 for x

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


Exponential function

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.


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