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Exponential Function

y = ab^x

exponential growth

increase starts slowly then increases very quickly to infinity

exponential decay

decreasing very quickly, but never reaching zero

common ratio

The ______________________ is the amount you MULTIPLY to get each new term in a sequence.

Base

the number that is written with an exponent

exponent

A mathematical notation indicating the number of times a quantity is multiplied by itself

7

What is the y-intercept of y=2(3)^x+5?

-4

What is the y-intercept of y=-2(1/2)^x -2?

y=5

Where is the horizontal asymptote for y=2(3)^x+5?

y=-2

Where is the horizontal asymptote for y=-2(1/2)^x -2?

Decay

Does y=-2(1/2)^x -2 represent exponential growth or decay?

50% decrease

What is the percent of decrease for y=-2(1/2)^x -2?

200% increase

What is the percent of increase for y=2(3)^x+5?

1.26

What growth factor represents a 26% increase?

2.5

What growth factor represents a 150% increase?

0.7

What decay factor represents a 30% decrease?

0.6

What decay factor represents a 40% decrease?

Increase

Is y=2(3)^x+5 an increasing or decreasing function?

y→∞ as x→∞

Describe the end-behavior for y=2(3)^x+5.

y→-2 as x→∞

Describe the end-behavior for y=-2(1/2)^x -2.

y→ ∞ as x→∞

Describe the end-behavior for y=(2.3)^x.

1

Give the y-intercept for y=(2.3)^x.

y=0

Give the horizontal asymptote for y=(2.3)^x.

130% increase

Give the percent of increase for y=(2.3)^x.

y→-∞ as x→∞

Describe the end-behavior for y=-2(1.8)^x+4.

y→0 as x→∞

Describe the end-behavior for y=25(0.8)^x.

y→7 as x→∞

Describe the end behavior for y=20(0.9)^x+7.

y=4

Give the horizontal asymptote for y=-2(1.8)^x+4.

(ab)^m=(a^m)(b^m)

Power of Product

(b^m)(b^n)=b^(m+n)

Product of Power

(b^m)^n=b^mn

Power of Power

(b^m)/(b^n)=b^(m-n)

Quotient of Power

(a/b)^m=(a^m)/(b^m)

Power of Quotient

b^0=1

Zero Power

b^-n=1/b^n

Negative Power

f(x) = -(3)^x

reflection across the x-axis, base is 3, a is 1, growth

g(x) = 4^(x-2)

horizontal shift to right 2 units, base is 4, a is 1, growth

h(x) = (1/2)^x+3

vertical shift up 3 units, base is ½, a is 1, decay

f(x) = (1/2)^-x

reflection across the y-axis, base is ½, a is 1, decay

f(x) = -(2^x) - 7

reflection across the x-axis, vertical shift down 7, base is 2, a is 1, growth

f(x)=2^(x+2)

horizontal shift left 2 units

f(x) = -(2^x)

reflects across the x-axis

f(x) = 2^x + 1

vertical shift up one unit

f(x) = 2^-x+3

reflects across the y-axis and shifts up three units

f(x) = 3 ∙ 2^x

stretches by a factor of 3

f(x)=1/2 ∙ 2^x

shrinks by a factor of ½

f(x)=-(1/2)^x - 6

reflects across the x-axis and shifts down 6 units