Properties of
Exponents
Exponents
Exponential
Functions
Functions
Exponential Growth
and Decay
and Decay
Finding Exponential Equations
Geometric
Sequences
Sequences
100
Any number or expression raised to the power of zero is always equal to _______.
1
100
What is the standard form of an exponential function?
y=a(b)^x
100
What does a represent in an exponential growth or an exponential decay function?
The initial (starting) amount
100
Find the exponential equation with a multiplier of 5 and a starting value of 2.5
y = 2.5(5)x
100
Geometric sequences have a common _______ between consecutive terms.
Ratio or multiplier
200
Simplify the expression. Write your answer using only positive exponents.
2^4*2^3
128
200
Tell whether the table represents a linear function or an exponential function. Explain.
Linear Function – as x increases by 1, y increases by 2
200
Does the following function represent exponential growth or exponential decay? Explain.
y=0.25(1.56)^t
Exponential Growth – the number is parentheses is larger than 1
200
find the exponential equation through the points (0,8) and (2, 2)
y = 8(1/2)x
200
Identify the common ratio of the following geometric sequence.
3, 18, 108, 648, . . .
r = 6
300
Simplify the expression. Write your answer using only positive exponents.
(x^5)^-3
1/x^15
300
Tell whether the table represents a linear function or an exponential function. Explain.
Exponential Function – as x increases by 4, y is multiplied by ½
300
Does the following function represent exponential growth or exponential decay? Explain.
y=–6(3/4)^t
Exponential Decay – the number in parentheses is between 0 and 1.
300
Find the exponential equation through the points (5,18) and (6, 13.5)
y = 886.89(.75)x
300
Identify the common ratio of the following geometric sequence.
144, –72, 36, –18, . . .
r = –½
400
Simplify the expression. Write your answer using only positive exponents.
4x^0y^-3
4/y^3
400
Evaluate the following exponential function when x = 3.
y=-8(4)^x
–512
400
Identify the percent rate of change of the following exponential function.
y=0.25(1.56)^t
r = 56%
400
Find the exponential equation through the points (2,6) and (6, 234.375)
y = .96(2.5)x
400
Write an equation for the nth term of the geometric sequence.
2, 8, 32, 128, . . .
a_n=2(4)^(n-1)
500
Simplify the expression. Write your answer using only positive exponents.
((2x^4y^2)/(5xy^6))^2
(4x^6)/(25y^8)
500
Evaluate the following exponential function when x = –4.
y=2(1/2)^x
32
500
Identify the percent rate of change of the following exponential function.
y=-6(3/4)^t
r = 25%
500
Find the exponential function through points (7, 12) and (12,36.63)
y = 2.517(1.25)x
500
Find the 6th term of the following geometric sequence.
0.6, –3, 15, –75, . . .
a_6=-1,875