Sequences & Function
What type of sequence is sequence b? Arithmetic, geometric, or neither
What is the common difference/ratio?
b: 56, 50, 44, 38, . . .
Type of Sequence: Arithmetic
Common Difference: -6
Simplify the following expression (no negative exponents in your final answer):
y^10\cdoty^-6
y^4
Find the solution(s) to the following equation:
x^3=8
x = 2
Evaluate the following radical (simplify completely):
3 \sqrt(8^2)
4
What is the initial value? Is this Exponential Growth or Exponential Decay?:
f(x) = 279(0.5)^x
279
Exponential Decay
Give the first 5 terms of the sequence with the following recursive definition:
f(1) = 5, f(n) = 6f(n-1), n>=2
f: 5, 30, 180, 1080, 6480
Simplify the following expression:
(x^2y^4)^3
x^6y^12
Find the solution(s) to the following equation:
x^2=4
x = 2 or x = -2
Rewrite in exponential notation:
4 \sqrt{3^3
3^{3/4}
What is the growth/decay rate?
f(x) = 564(1.023)^x
Write the recursive definition of the following sequence g (assume the sequence starts at Step 1):
g: 24, 12, 6, 3, . . .
Recursive Definition:
g(1) = 24, g(n) = 1/2g(n-1), n>=2
Simplify the following expression (no negative exponents in your final answer):
x^5/x^6
1/x
How many solutions are there for the following equation, and what are the solution(s)?:
(x+5)^3= -27
1 solution
x = -8
Rewrite in radical notation:
15^{5/7}
7 \sqrt(15^5)
A town has a population of 18,000 people. The population decreases by 2.4% each year. What will the population be in 15 years? Round to the nearest whole number.
12503 people
Write the explicit definition of the sequence j and describe how the sequence is changing (assume the sequence starts at Step 0 or n=0):
j: 4, 7, 10, 13, . . .
Explicit Definition:
j(n) = 4+3n, n>=0
Simplify the following exponential expression (no negative exponents):
(2x^2y^4)\cdot(3x^7y)
6x^9y^5
How many solutions are there for the following equation, and what are the solution(s)?:
(x-2)^2=64
2 solutions
x = 10 or x = -6
Write the following radical in exponential notation (negative exponents okay here):
1/\sqrt{3^5}
3^(-5/2)
A bacteria culture starts with 500 bacteria. The population doubles every 3 hours. What is the growth factor of the bacteria culture every hour?
2^(1/3
Find the 19th term of the following sequence k (assume sequence k starts at Step 1):
k: 0.25, 0.5, 1, 2, . . .
19th term of sequence k:
65,536
Simplify the following expression (There should be no negative exponents) and describe what exponent rules you used:
\frac{15x^5y^8z^4}{5x^7y^7z^4
\frac{3y}{x^2}
How many solutions are there to the following equation and what are the solution(s)? Explain why it has the number of solutions that it has:
5(x+1)^2-3=17
2 solutions
x = 1 or x = -3
Find the 2 whole numbers closest to \sqrt(94) Explain your reasoning.
The 2 whole numbers closest to \sqrt(94) are 9 and 10 because \sqrt(94) is between \sqrt(81)=9 and \sqrt(100) = 10
WORTH A 1000 POINTS!
The function m , defined by m(h) = 1000(4/5)^h , represents the population of a town. h represents the number of years that has passed. If the town had a population of 1000 in year 2009, what does m(6) represent? Explain what m(6) represents.
m(6) represents the population of the town in the year 2015 or 6 years after 2009.