Rational Exponents & Radicals *NO calc
Exponents Properties
*NO calc
*NO calc
Exponential Functions, Growth/Decay
Sequences
Hodge Podge
100
A rational exponent has an exponent in the form of a ________.
fraction
100
Simplify.
8^-2
1/64
100
What is the general form of an exponential function?
f(x)=abx
100
A geometric sequence increases by a constant called the ____________ (r).
common ratio
100
Simplify.
(4x^2y^3)(-4xy^2)
-16x^3y^5
200
TRUE or FALSE:
To rewrite a rational exponent as a radical, use the formula:
rootn(a)=a^(1/n
True
200
Simplify.
(2a^2b^3)^3
8a^6b^9
200
The graph on the right represents an exponential decay function.
The base of an exponential decay function is between the numbers ____ and ____.
0 and 1
200
a) Identify the common ratio in the sequence:
3, -6, 12, -24, 48, ...
b) Identify the common difference in the sequence:
-1, 4, 9, 14, 19, ...
a) r= -2 & b) d = +5
200
Tell whether the table is arithmetic, geometric or neither.
arithmetic
300
Rewrite the exponent in radical form, then simplify:
125^(1/3)
5
300
Simplify.
((2x^-3)/(5x))^-3
(125x^12)/8
300
Multiple Choice. Which function represents exponential decay?
C
300
One of the graphs represents an arithmetic sequence and the other represents a geometric sequence. Which graph represents a geometric sequence, the red or green function?
the red one
300
What is the next term in the sequence?
2, 4, 6, 10, 16, 26, 42, _____
68
400
Rewrite the exponent in rational form, then simplify:
16^(1/4)+32^(1/5)
4
400
Simplify.
(6d^-2)^0
1
400
Using the exponential growth model, y=a(1+r)t, write a function for the situation: A football card is sold for $2, and its value increases by 8% each year after it is sold. Then find it's value after 25 years.
y=2(1.08)t
Value after 25 yrs: $13.70
400
The first two terms of a sequence are a1=-2 and a2=4. Let a3 be the third term when the sequence in arithmetic and let b3 be the third term when the sequence is geometric. What is a3 + b3?
a3 = 10, b3 = -8
So a3 + b3 = 2
400
Mr. Sanchez has $5000 in his savings account and has been earning interest at a rate of 5.5%, compounded monthly. How much INTEREST did he make on his $5000 over 10 years?
$3,655.38 (Total in account is $8,655.38 so his INTEREST earned is $3,655.38)
500
Rewrite in radical form, then simplify:
25^(-1/2)
1/5
500
Simplify.
root3(27)+root4(16)+root6(64)
7
500
Write an equation for this situation.
The value of your Algebra I textbook is $65 and decreases at a rate of 15% per year for 11 years. What is the value after 11 years?
y=65(.85)t
$10.88
500
Write an explicit rule for the sequence:
16, -3.2, 0.64, ...
f(x)=16(-0.2)n-1
500
You create a social media post and tag 7 friends. In the second round, each of your friends tag 7 friends and the process continues. How many people will be tagged in the sixth round?
76 = 117,649 people