Exponents 7.1
Exponents 7.2 & 7.4
Word Problems
Exponents 7.3
Exponential Functions
100
Determine whether this expression is a monomial. Explain why or why not.
3a4
Yes, it is a product of constants and variables.
100
Express the answer in both standard form and scientific notation.
(2 * 10^3)(6*10^3)
1.2*10^7; 12,000,000
100
Paige invested $1200 at a rate of 5.75 % compounded quarterly. Determine the value of her investment after 7 years.
$1,789.54
100
Write in radical form:
3x^{1/4}
3 root(4){x}
100
Is the function below exponential? Explain why or why not.
x | y
-6 | 8
-3 | 4
0 | 2
3 | 1
Yes, it is exponential because we are multiplying by 1/2 each time!
200
Determine whether this expression is a monomial. Explain why or why not.
3 + a4
No, it is not a product, it is a sum which is not just one term.
200
Express the answer in both standard form and scientific notation.
\frac{2 * 10^{-8}}{4 * 10^{-2}}
5 *10^{-7}; 0.0000005
200
Camilo purchased a rare coin from a dealer for $300. The value increases at 5% each year. Write an equation to model the value over time. Use the equation to find the value after 5 years.
y =300*(1.05)^x, \$ 382.88
200
Write in exponential form:
3 sqrt(xy)
3 (xy)^{1/2}
200
Is the function below exponential? Explain why or why not.
x | y
-6 | 8
-3 | 6
0 | 4
3 | 2
No, it is not exponential. It is linear because it is changing at a constant rate of -2/3. It is not multiplying by the same number each time.
300
Determine whether this expression is a monomial. Explain why or why not.
k/2
Yes, it is a monomial because it can be written as 1/2 * k which is a product of constants and variables
300
Simplify:
\frac{r^4t^7v^2}{t^6v^5}
\frac{r^4t}{v^3}
300
Leonardo purchases a car for $18,995. It depreciates at a rate of 18% per year. Create an equation to represent the car's value over time. After 6 years how much is it worth?
y = 18995*(0.82)^x, \$5,774.61
300
Simplify:
25^{3/2}
125
300
Graph and find the y-intercept, domain, and range:
y = -5^x
D: {all real numbers}
R: { y < 0}
y-int: (0, -1)
400
Simplify:
(5u^4v)(7u^4v^3)
35u^8v^4
400
Simplify:
\frac{2a^2b^{-7}c^10}{6a^{-3}b^2c^{-3}}
\frac{a^5c^13}{3b^9}
400
Jin's investment of $4,500 has been losing value at a rate of 2.5 % each year. Create an equation to represent the value of the investment over time and find the value after 5 years.
y = 4500 (1- 0.025)^x, \$3,964.93
400
Simplify:
9^{-\frac{3}{2}}
\frac{1}{27}
400
Graph and find the y-intercept, domain, and range:
y = 6^x-3
D: {all real numbers}
R: { y > -3}
y-int (0, -2)
500
Simplify:
(4x)^2 (x^3y)^3(y^5)
16x^{11}y^8
500
Simplify:
\frac{(x^2y^{-4}z^5)^0}{(2x^-5y^7z^5)^{-2}}
\frac{4y^{14}z^{10}}{x^{10}}
500
Danielle's parents have offered her two different options to earn her allowance for a 9 week period over the summer. She can either get paid $30 each week or $1 the first week, $2 the second week, $4 the third week, and so on. Find the total she would get paid with each option. Which should she choose?
$270 with the first and $511 with the second. She should choose the second one because she will earn $241 more.
500
Solve for x:
5^x = \frac{1}{25}
x = -2
500
Graph and find the y-intercept, domain, and range:
y = 3(1/4)^x
D: { all real numbers}
R: {y >0}
y-int (0, 3)
600
Write three different expressions that can be simplified to x6 that demonstrate three different exponent rules.
ex. x4*x2
(x3)2
x9/x3
600
Simplify:
(\frac{-3x^{-6}y^{-1}z^{-2}}{6x^{-2}yz^{-5}})^{-2}
\frac{4x^8y^4}{z^6}
600
Jonah invests $1,000 and wants his money to triple over the next 10 years. What would the interest rate need to be if it is compounded monthly?
About 11%
600
Solve for x:
4^(2x-1) = 32^x
x = -2
600
When does the graph of the equation below have a y - intercept? (a is not 0, b is positive and not 1)
y = a*b^x
Never. It would need to be equal to 0 to have an x-intercept and a*bx can never be 0 because something to a power can't be equal to 0. It just gets closer and closer to 0 but never gets there. Think of taking half of something every day, it will never get to zero, there will always be some part left!
700
Name two monomials with a quotient of 15a4b3
ex. 30a5b5 and 2ab2
700
Solve for x:
(1/4)^{x-1} = 8^{2x+1}
x = -1/8