Linear Functions
Exponential Functions
Linear or Exponential?
Slope/Average Rate of Change
Simplifying Expressions
100
What is the equation in slope-intercept form for a linear function? Define the parts of the equation.
What is...
y = mx +b ; where m=the slope and
b=the y-intercept, or the initial value.
100
What is the standard formula for an exponential function?
What is...
y=abx where a is the initial value of the function (the y-intercept) and b is the constant growth/decay factor (common ratio).
100
Linear or exponential? Write the equation
At the start of a carnival, you have 70 ride tickets. Each time you ride the roller coaster, you have to pay 6 tickets.
What is...
Linear.
y=-6x+70
100
What is the slope during part C? (include units)
What is...
40 miles per hour.
100
(16x^8)/(2x^2
8x^6
200
What is the equation to find the slope?
What is...
The change in y-values over the change in x-values or m = (y2 - y1)/(x2 - x1).
200
The height of a bouncing ball (in feet) after x bounces can be modeled with the function:
y=12(.75)x
What is the height of the ball after the first bounce?
What is...
9 feet.
200
Linear or exponential? Write the equation.
“A bank account starts with $10. Every month the amount in the account is tripled.”
What is...
Exponential
y=10(3)x
200
What is the slope for part E? (include units)
What is...
-60 miles per hour
200
(4x^3y^2z^3)^-2
1/(16x^6y^4z^6)
300
What does the slope of a linear function represent? Does it change or is it constant for a linear function?
What is...
The rate of change between variables (often expressed as a "per" phrase like "miles per hour".
For a linear function, slope is constant.
300
Write the equation for a function that starts with 5 and doubles every day.
What is...
y=5(2)x
300
Linear or Exponential? Write the equation.
In 1990, 600,000 people lived in Washington D.C. The population is increasing about 2% per year.
What is...
Exponential
y=600,000(1.02)x
300
What is the average rate of change between the two points?
What is...
Average Rate of Change: -1/2
300
(x^3y^4)^3*(3xy^2)^2
9x^11y^16
400
Write a linear function that shows the relationship between cost and number of months:
Orland buys a gym membership that costs $40 upfront and then $20 each month after.
What is...
y = 20x + 40
400
What would the equation for the scenario below be?
Brandon has a bank account with $20,000 in it. Each year it earns 5% in interest.
What is...
y = 20,000(1.05)x
400
Linear or exponential? Solve it.
A roller skating rink charges $15 to rent skates and $8 per hour to skate. How much money did you spend if you skate for 4 hours?
What is...
Linear.
$47
400
Find the average rate of change in the given table for the interval of x=5 and x=20.
What is...
Average Rate of Change = $8 per car
400
(4b^2c^3 * 3bc^5) / (6b^3c^10)
2/c^2
500
Write a function that shows the relationship between the number of rides she goes on and the number of tickets she has:
Maya goes to the county fair. She has 57 tickets when she gets there and each ride costs 3 tickets.
What is...
y = -3x + 57
500
I deposit $120 in an account and I double the amount every year. Write the equation to calculate the amount in the account after 5 years.
What is...
y=120(2)5
500
Linear or exponential? Solve it
Suppose you accidentally open a canister of plutonium in your living room and 160 units of radiation leaks out. If every year, there is half as much radiation as there was the year before how many units of radiation will there be after 4 years?
Linear or exponential? Write the equation to calculate the tractor's value after x years.
What is...
Exponential.
10 units
500
Find the average rate of change between the given values of the variables:
f(x)=2x2-10
t=2 t=5
What is...
Average Rate of Change = 14
500
(4b^2c^3 * 3bc^5)^3 / (6b^3c^10)
2b^6c^14