Zeroes, Negatives, and rational exponents
What is any number to the 0 power?
What is 3^2*3^5 ?
3^7
simplify (8a^8)/(2a^2)
4a^6
What is a principal root?
The positive square root of a number
Convert 7.21 times 10^5 to scientific notation.
721,000
When investing money in a bank account, in which situation will you have the most money in your account at the end of two years? Compounding weekly, monthly, yearly, or semiannually?
What is the approximate value of e?
What is a geometric sequence?
A sequence where each term is multiplied by a common ratio to find the next term
Describe the differences in the graphs of linear functions vs. exponential functions.
Linear functions have a constant rate of change. Exponential functions have a rate of change that varies over time
Evaluate 5^(-2)
1/25
simplify a^3a^10
a^13
simplify (y^-2)/(3y^4)
1/(3y^6)
What is the principal square root of 36
6
The average red blood cell has a thickness of 0.0000024 m. Write this number in scientific notation.
2.4 times 10^-6
You invest $500 in an account that has a annual interest rate of 5%, compounded quarterly for four years. How many times will the money be compounded?
16 times
Solve the equation y = ex for x.
x = ln(y)
Determine if the sequence 5, 15, 45, 135, 405, ... is geometric. If so, what is the common ratio. If not, what is the pattern?
Geometric with a ratio of 3.
You win a prize and are offered two choices. Which of the choices could be represented by a linear equation?
Choice A: $0.10 on January 1, $0.20 on January 2, $0.40 on January 3, $0.80 on January 4, and so on, with the amount doubling each day.
Choice B: $5.00 on the first day, $10.00 on the second day, $15.00 on the third day, and so on, with $5.00 added each day.
Choice B
What expression represents x^-a
1/x^a
simplify (2x^2)(3x^3)
6x^5
Simplify (p^8q^3)/(p^4q^12)
p^4/q^9
rewrite x^(7/5) as a radical
root(5)(x^7)
Is 7.2 times 10^2.5 written correctly in scientific notation?
You invest an initial $100 in an account that has an annual interest rate of 3%, compounded quarterly. How much money will you have in the account after 20 years?
100(1+.03/4)^((4)(20))
100(1.0075)^(80)
100(1.818)
$181.80
The population in Smalltown in 2010 was 45,230 people and is growing exponentially at a rate of 2 percent. Write a simple exponential function to represent the population in t years.
45320e^(.02t)
What is the formula for the nth term of a geometric sequence?
a_n = a_1 cdot r^(n-1)
The population of a large city can be calculated using the function P=156,000(1.07)^x . What can you say about the rate of change from year 1 to year 2 compared to the rate of change from year 9 to year 10?
The rate of change will be larger from years 9 to 10
Simplify 16^(3/2)
sqrt(x^3)
Simplify (2x^2)^3
8x^6
Divide 12xy^3z^6 by 4x^5yz^12
3x^-4y^2z^-6
(3y^2)/(x^4z^6)
simplify root(3)(-216)
-6
Define scientific notation
hint: define a and b in a times 10^b
a times 10^b
Where a is a number between 1 and 10, and b is an integer
You invest an initial $300 in an account that has an annual interest rate of 4%, compounded quarterly. How much money will you have in the account after 10 years?
$447
Who was the number e both discovered by and named after?
Leonard Euler
Give the 10th term in the geometric sequence: 2, 6, 18, 54, ...
a = 2; r = 3; a_n = a_1 cdot r^(n-1)
a_10= 2•3^(9)
a_10 = 39,366
What is the exponent of a linear function?
1
Simplify 25^(7/3)
root(3)(x^7)
Simplify (g^4h)^6
g^24h^6
Give the mathematical definition of the product of powers property.
(x^m)/(x^n) = x^(m-n)
The volume of a cube is 8 square inches, what is the length of 1 side?
2 inches
Divide 4.2 times 10^9 by 4.62 times 10^3
(4.2 times 10^9)/(4.62 times 10^3) = (4.2/4.62)times(10^9/10^3)=
0.91 times 10^6 =
9.1 times 10^5
You have $1,000 to invest in an account, and need to have $1,500 in one year. What interest rate would you need to have in order to reach this goal if the amount is compounded quarterly?
1500 = 1000(1+x/4)^4
1500/1000 = (1+x/4)^4
1.5 = (1+x/4)^4
root(4)1.5 = 1+x/4
1.107 = 1+x/4
0.107 = x/4
x = 0.4267 = 42.67%
What is the expression that e represents?
(1+1/n)^n
Find the first four terms of the geometric sequence whose nth term is a_n = −2(4)^(n −1).
-2, -8, -32, -128
A plumber charges a fee of $25 plus $30 per hour on the job. Determine if this can be defined by a linear or an exponential function. What is the function?
Linear, T = 25 + 30h