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Level 398

Exponential Functions


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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