Exponents & Radicals
6.3 - Exponential Functions
6.4 Growth and Decay
6-6 Transformations
Arithmetic or Geometric Sequences
100
Rewrite the expression using exponents:
root(4)(12^3)
12^(3/4)
100
If, y=a(b)x , what does 'a' represent?
a=initial amount or y-intercept
100
Does the graph represent exponential growth or decay?
Exponential Growth
100
How do these graphs differ?
f(x) = 2^x
f(x) =2^x + 5
Translate up 5 units
100
Is the following sequence arithmetic or geometric?
2,8,14,20,16...
Arithmetic
200
Simplify completely:
3sqrt(6)
200
What is the initial value for the function?
What is the constant ratio for the function?
f(x)=2(3)x
2 ,3
200
f(x)=-4(1.07)x
Does this functions represent exponential growth or decay? What's the percent growth/decay factor?
Exponential Growth. 7%.
200
How do these graphs differ?
f(x) = 3^(x+2)
Translate left 2
200
Is the following sequence arithmetic or geometric?
5,10,20,40,80...
geometric
300
Simplify completely:
(x^(1/2))(x^(1/4))
x3/4
300
What is the equation of this graph?
y= 1(2)x or just y = 2x
300
How much money would Lisa have after 10 years if she invest $12,000 at an annual interest raet of 5% compounded semiannually?
$19663.40
300
What features will remain the same between the two functions? Domain? Range? Y-intercept? Aymptote?
f(x)= 2^x
f(x)= 1/2(2)^x
domain, range, and asymptote
300
Is this arithmetic or geometric and what is the common ratio or difference?
100,50,25,12.5...
geometric 2
400
Simplify completely:
12^(2/3)/12^(1/6)
12^(1/2)
400
Identify the key features of this graph:
Initial value, Constant ratio, Domain, Range, & Asymptote
f(x)= 12(0.5)^x
a:12
b:0.5
D:All real #'s
Range: y>0
Asymptote:y=0
400
Write an equation to represent a town with an initial population of 1,400 people and an annual growth rate of 6%. What will the population be in 3 years?
f(x)= 1400(1.0125)x
1667
400
How does the graphs of the functions differ?
f(x) = 5^(x-2) - 5
Down 5 right 2
400
Write the recursive formula for the following sequence.
1,5,9,13,17...
a1=1
an=an-1+4
500
Simplify completely:
sqrt(32x^4y^3)
4x^2ysqrt(2y)
500
What's the equation for this table?
y=5(2)x
500
Ms. Wiggins purchased a car for 26,400 and every year it decays by 12%. Write an equation to represent this situation.
When will the car be less that 10,000?
f(x)=26400(.88)t
8 years
500
What is the aymptote and y intercept of the function?
f(x)= 0.8^x -10
y=-10
y intercept (0,-9)
500
Write the explicit formula and find the 10th term for the following sequence.
1,3,9,27,81...
an=1(3)n-1