Linear or Exponential?
Discrete or Continuous?
Domain
Linear Equations
Exponential Equations
100
f(x) = f(x - 1)⋅2 ; f(4) = 16
Exponential because there is a ratio of 2.
100
An arithmetic sequence with a common difference of 4.
Discrete because all sequences are discrete!
100
Of an arithmetic sequence
All whole numbers
100
Write the equation of a line with a slope of 3/4 and a y-intercept of -1 in slope intercept form.
f(x) = 3/4x - 1
100
Write the equation of an exponential function with a ratio of 4 and f(1) = 5.
f(x) = 5(4)x-1
200
f(x) = 1/3(x - 4) + 7
Linear - point slope form
200
Your total savings after you get your biweekly paycheck from work.
Discrete. Your savings immediately increases by the amount that you were paid.
200
Height over time
All positive real numbers (independent variable is time)
200
Write the equation of a line through the point (1,2) with a slope of -3 in point slope form.
f(x) = 2 - 3(x - 1)
200
The grocery store reduces the price of baked goods by 10% every day. Write an equation to model the price of a cake originally marked as $30.
f(x) = 30(.9)x
300
An air mattress losing 20% of its air each minute as it deflates.
Exponential - just like anything with a percent!
300
The length of your hair over time
Continuous - hair gradually grows
300
All real numbers!
300
Write the equation of the line through (4, 5) and (-3, -2)
f(x) = 5 + 1(x - 4)
300
One of my stocks increased its value by 6% this year. I originally invested $3,000. Write an equation to model the stocks worth each year if it continues this same growth.
f(x) = 3,000(1.06)x
400
A pool filling up at a rate of 4 gallons per minute
Linear - there is a constant rate of change
400
The temperature throughout the course of a day
Continuous - temperature gradually increases or decreases. It does not skip any values.
400
The amount of screen time you get a day and the quality of your sleep
All positive real numbers (independent variable is time)
400
Water traveling down a stream at a rate of 30 miles per hour.
d(t) = 30t (where t is time in hours, and d(t) is distance traveled)
400
Write the equation of the graph: 
f(x) = 2x
500
f(x) = 4(10)x - 3
Exponential - ratio of 10
500
Profit made from selling $15 homecoming shirts for the class of 2025
Discrete - we make $15 at a time, all at once.
500
Paige hands me 2 life savers each day.
All whole numbers (independent variable = days)
500
Write the equation of the line:
f(x) = 1/2x + 1
500
Write the equation of the exponential function that goes through (0, 1) and (1, 4)
f(x) = 4x