Linear Functions
Linear Functions
Linear or Exponential?
Exponential Functions
Exponential Functions
100
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
100
In the equation y= 3x + 7, name the y-intercept.
State your answer in the form of a point (x, y)
What is...
(0, 7)
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
The standard formula for an exponential function is y=b*rx or y=b(1+r)x if it is changing by a percentage.
In either case, what does "b" represent?
What is...
The initial value of the function (the y-intercept)
100
What is then standard equation for exponential functions? Describe each part.
What is...
y = b • rx where b=initial value and r=growth factor
y = b • (1+r)x where b=initial value and r=% growth factor, which can be negative for decay
200
What is the equation in slope intercept form for a linear function? Define the parts.
What is...
y = mx +b
Where
m=the slope and
b=the y-intercept, or the initial value
200
Monica is saving her weekly allowance ($) to buy a gift for her brother. Her savings is modeled by the function:
y = 2x + 5
What is the slope? (Include units in your answer)
What is...
$2 per week
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 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
y = 20,000(1.05)x
200
When would this function be used:
y=b*(1/2)^(t/10)
a problem that involves a half-life of 10 (years, minutes, days, ...)
300
What is the equation or process to find the slope?
What is...
The change in y-values over the change in x-values or
m = (y2 - y1)/(x2 - x1)
300
What is the slope during part B? (include units)
What is...
0 miles per hour
300
Linear or Exponential? Write the equation.
In 1990, 600,000 people lived in Washington D.C. The population is increasing about 1.02% per year.
What is...
Exponential
y=600,000(1.02)x
300
Explain the difference between linear and exponential functions.
What is...
Linear functions have a constant rate of change (slope). The value of the function changes by adding or subtracting the same amount repeatedly.
Exponential functions have a slope that is always changing. The value of the function changes by multiplying by the same amount repeatedly.
300
Write the equation for a function that starts with 5 and doubles every day.
What is...
y=5(2)x
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.
y = 20x + 40
400
what is the slope during part C? (include units)
What is...
40 miles per hour
400
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?
What is...
Exponential.
10 units
400
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
400
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
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
What is the slope for part E? (include units)
What is...
-60 miles per hour
500
Linear or exponential? Write the equation to calculate the tractor's value after x years.
My tractor costs $12,500. It's value depreciates by 93/100 each year.
What is...
Exponential
y=12,5000(0.93)x
500
The population of a city is decreasing by 97/100 each year, where x is the number of years since the last census. The population was 47,500 at that time.
Write the equation that shows the population after 10 years.
What is...
y=47,500(97/100)x
500
In the March Madness basketball tournament, 64 teams play against one another. Only the winning teams progress to the next round. In other words, the number of teams playing at after round is half of the number of teams playing in the previous round. How many teams are left after 4 rounds?
What is...
4 teams