Domain and Range of Functions
Simplifying Exponentials/Radicals
Properties of Exponential Functions
Method of Common Bases
Exponential Modeling
Definitions and Processes
Finding Equations of Exponentials
100
What is the domain and range of the function:
y=5x+2?
Domain: (-∞,∞)
Range: (-∞,∞)
100
Simplify the following exponential expression so that there is only one base and one exponent:
2^4*2^x
2^(4+x)
100
Evaluate the following function when x=4:
y=2*3^x-5
157
100
Find the value of x from the following equation:
2^5=2^(x+1)
x=4
100
Your local bank is offering a checking account with 1.2% interest per year. You decide to deposit $100 in this account. What are your initial value and percentage increase?
initial value: $100
percentage: 1.2 or 1.2%
100
What is a base? What is an exponent? Provide an example.
b^x
b is the base, x is the exponent
100
If the initial value of an exponential is 5 and the base is 3, what is the exponential equation?
y=5(3)^x
200
What is the domain and range of the function:
y=4?
Domain: (-∞,∞)
Range: 4
200
Rewrite the following exponential in radical form:
3^(5/3)
root(3)(3^5)
200
Is the following exponential function increasing or decreasing as x goes to infinity? Explain your answer.
y=5*(1/2)^x+3
Decreasing, as the base is a number between 0 and 1.
200
Find the value of a in the following equation:
3^4=9^(a+3)
a=-1
200
Suppose you're studying a virus strain that creates 4 new viruses every hour. You start your study by injecting 5 viruses into a lab rat. After 5 hours, how many viruses will there be in the rat?
5120 viruses
200
What is an asymptote? Provide an example.
A line that a function approaches but doesn't ever touch.
200
An exponential function contains the points (0,7) and (4,102). What is this exponential function?
y=7(1.95)^x
300
What is the domain and range of the following:
y=5(4)^x
Domain: (-∞,∞)
Range: (0,∞)
300
Simplify the following exponential expression so that there is only one base and one exponent:
(3^x/3^2)^5
3^(5x-10)
300
What is the domain and range of the following exponential function:
y=5*2^x
Domain: (-∞,∞)
Range: (0,∞)
300
Find the value of y in the following equation:
3^(y-2)=9^(5y+7)
y=-16/9
300
Meg just bought a new cell phone worth $800! She's thinking about eventually selling it to help her upgrade to another phone, but knows that her phone will lose 8% of its value every year. Approximately how many months will it take for her phone to be worth only $600? (round to the nearest month)
41 months
300
When you are given two points on an exponential function, how do you find that function? Provide the steps you need to perform.
1. Plug in the points into the equation y=a(b)^x and create two different equations.
2. Divide one equation by the other to isolate for b.
3. Solve for b.
4. Plug b back into one of the equations you created to solve for a.
300
An exponential function contains the points (1,12) and (3,108). What is the exponential function?
y=4(3)^x
400
What is the domain and range of the function:
(1/2)^x+3
Domain: (-∞,∞)
Range: (3,∞)
400
Simplify the following exponential expression so that there is only one base and one exponent:
(3^2*9^9)/27^2
3^14
400
What line represents the asymptote of the function:
y=4^x+3
y=3
400
Find the value of t for the following equation:
4^(2t+3)=32^(t-1)
t=11
400
We're trying to find the best savings account to put our money in for the next 10 years. The Bank of Nemo offers a plan where if you deposit $200, the account gets an interest rate of 2.3%. The Bank of Dory offers a plan where if you deposit $220, the account gets an interest rate of 2%. Which bank's savings account would be better for us?
Bank of Dory
400
When you are given an exponential equation with exponentials of different bases, how do you solve for a variable in the exponent?
1. Find a common base for all exponentials (choose the smallest convenient base, convert larger bases into the smaller bases).
2. Using exponent properties, combine the exponentials so that there is only one exponential on each side of the equation.
3. Set the exponents of the exponentials in step 2 equal to each other and solve for the variable.
400
Mushu and Mulan are launching fireworks to celebrate the holidays. They find that 1 second after a firework has taken off, it is 10 feet in the air. After 4 seconds, the firework is 80 feet in the air. What is the exponential equation that best represents the firework's height?
y=5(2)^x
500
What is the domain and range of the function:
-3^(-x+2)-1
Domain: (-∞,∞)
Range: (-∞,-1)
500
Simplify the following expression so that there is only one exponential with one base and one exponent:
(x^(1/3)*root(3)(x^2))^(3x+1)
x^(3x+1)
500
Is the following exponential function increasing or decreasing as x goes to -∞? Explain how you can tell mathematically.
y=-5(1/3)^x+2
Decreasing, without the negative sign our function would increase as we got to negative infinity. With the negative sign, our function flips over the x-axis and decreases as it goes to negative infinity.
500
Find the value of z in the following equation:
(4^(2z+2))^3=2^(3z)*8^3
z=-1/3
500
Elsa and Anna are running for class president, and have agreed to hold multiple debates so their classmates can hear their plans. Elsa is more popular and starts with 120 supporters but loses 10% of her supporters each debate as she doesn't do well in public speaking. Anna starts with 50 supporters but gains 12% more supporters each time she participates in a debate. After how many debates will the two candidates have the same number of supporters? (round to the nearest integer)
4 debates
500
What is the domain and range of a basic exponential function? Example:
y=2^x
AND what could you change to a basic exponential function to change the range?
Domain: (-∞,∞)
Range: (0,∞)
You can add or subtract a number from the exponential function to change the range.
500
Naveen and Tiana are watching a frog hop along the side of a pond. After 3 minute of hopping, the frog had traveled 20 feet. After 5 minutes of hopping, the frog had traveled 40 feet. What is the exponential function that best represents this frog's distance traveled? Round any numbers in your final answer to the nearest hundredth.
y=7.07(1.41)^x