text: # Warm Up - DanPrest
  
  ```GRAPHING LINEAR
  EQUATIONS
  Linear Equations
  • Independent variable (x): the quantity that
  changes based on values you choose
  • Dependent variable (y): the quantity that is based
  on the input values of the independent variable
  Warm Up
  Steps for creating linear equations:
  2. Determine the known quantities.
  3. Identify the slope and the y-intercept.
  4. Substitute the slope and y-intercept into the
  equation y=mx+b.
  5. Graph the equation.
  1. A local convenience store owner spent \$10 on pencils to resell
  at the store. What is the equation that store’s revenue if each
  pencil sells for \$0.50? Graph the equation using a table of values.
  2. A taxi company in Atlanta charges \$2.50 per ride plus \$2 for
  every mile driven. Write and graph the equation (using the slope
  and y-intercept) that models this scenario.
  3. Miranda gets paid \$300 a week to deliver groceries. She also
  earns 5% commission on any orders she collects while out on her
  delivery run. Write an equation that represents her weekly pay
  and then graph the equation.
  4. A Boeing 747 starts out a long flight with about 57,260 gallons
  of fuel in its tank. The airplane uses an average of 5 gallons of
  fuel per mile. Write an equation that models the amount of fuel in
  the tank then graph the equation using a graphing calculator.
  5. You can buy a 6-hour phone card for \$5, but the fine print says
  that each minute you talk actually costs you 1.5 amount of time.
  What is the equation that models the number of minute left on the
  card compared with the number of minutes you actually talked?
  What is the graph of this equation?
  Warm Up
  One form of the element beryllium, beryllium-11, has a half-life of about
  14 seconds and decays to the element boron. A chemist starts out with
  128 grams of beryllium-11. She monitors the element for 70 seconds.
  1. What is the equation that models the amount of beryllium-11 over
  time?
  2. How many grams of beryllium-11 does the chemist have left after 70
  seconds?
  GRAPHING
  EXPONENTIAL
  EQUATIONS
  Exponential Equations Review
  • General form:
  • Growth: the base is greater than 1
  • Decay: the base is between 0 and 1
  Compound Interest
  • A: initial value
  • P: principle amount
  • r: interest rate
  • n: number of years
  Compound Interest Cheat Sheet
  Compounded…
  n (number of times per year)
  Year/annually
  1
  Semi-annually
  2
  Quarterly
  4
  Monthly
  12
  Weekly
  52
  Daily
  365
  1. If a pendulum swings to 90% of its height on each swing and
  starts out at a height of 60 cm, what is the equation that models
  this scenario? What is its graph?
  2. The bacteria Streptococcus lactis doubles every 26 minutes in
  milk. If a container of milk contains 4 bacteria, write an equation
  that models this scenario and then graph the equation.
  3. An investment of \$500 is compounded monthly rate of 3%.
  What is the equation that models this situation? Graph the
  equation.
  Warm Up
  ```
explanation: The document is a set of warm-up exercises and problems related to graphing linear and exponential equations. It includes several questions that require the creation and graphing of equations based on given scenarios. Each question is designed to test the understanding of linear and exponential functions, their applications, and how to graph them.
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distilabel_metadata.role: system
distilabel_metadata.content: # Warm Up - DanPrest
  
  ```GRAPHING LINEAR
  EQUATIONS
  Linear Equations
  • Independent variable (x): the quantity that
  changes based on values you choose
  • Dependent variable (y): the quantity that is based
  on the input values of the independent variable
  Warm Up
  Steps for creating linear equations:
  2. Determine the known quantities.
  3. Identify the slope and the y-intercept.
  4. Substitute the slope and y-intercept into the
  equation y=mx+b.
  5. Graph the equation.
  1. A local convenience store owner spent \$10 on pencils to resell
  at the store. What is the equation that store’s revenue if each
  pencil sells for \$0.50? Graph the equation using a table of values.
  2. A taxi company in Atlanta charges \$2.50 per ride plus \$2 for
  every mile driven. Write and graph the equation (using the slope
  and y-intercept) that models this scenario.
  3. Miranda gets paid \$300 a week to deliver groceries. She also
  earns 5% commission on any orders she collects while out on her
  delivery run. Write an equation that represents her weekly pay
  and then graph the equation.
  4. A Boeing 747 starts out a long flight with about 57,260 gallons
  of fuel in its tank. The airplane uses an average of 5 gallons of
  fuel per mile. Write an equation that models the amount of fuel in
  the tank then graph the equation using a graphing calculator.
  5. You can buy a 6-hour phone card for \$5, but the fine print says
  that each minute you talk actually costs you 1.5 amount of time.
  What is the equation that models the number of minute left on the
  card compared with the number of minutes you actually talked?
  What is the graph of this equation?
  Warm Up
  One form of the element beryllium, beryllium-11, has a half-life of about
  14 seconds and decays to the element boron. A chemist starts out with
  128 grams of beryllium-11. She monitors the element for 70 seconds.
  1. What is the equation that models the amount of beryllium-11 over
  time?
  2. How many grams of beryllium-11 does the chemist have left after 70
  seconds?
  GRAPHING
  EXPONENTIAL
  EQUATIONS
  Exponential Equations Review
  • General form:
  • Growth: the base is greater than 1
  • Decay: the base is between 0 and 1
  Compound Interest
  • A: initial value
  • P: principle amount
  • r: interest rate
  • n: number of years
  Compound Interest Cheat Sheet
  Compounded…
  n (number of times per year)
  Year/annually
  1
  Semi-annually
  2
  Quarterly
  4
  Monthly
  12
  Weekly
  52
  Daily
  365
  1. If a pendulum swings to 90% of its height on each swing and
  starts out at a height of 60 cm, what is the equation that models
  this scenario? What is its graph?
  2. The bacteria Streptococcus lactis doubles every 26 minutes in
  milk. If a container of milk contains 4 bacteria, write an equation
  that models this scenario and then graph the equation.
  3. An investment of \$500 is compounded monthly rate of 3%.
  What is the equation that models this situation? Graph the
  equation.
  Warm Up
  ```
distilabel_metadata.role: user
distilabel_metadata.raw_output_q_a_detector_0: The document is a set of warm-up exercises and problems related to graphing linear and exponential equations. It includes several questions that require the creation and graphing of equations based on given scenarios. Each question is designed to test the understanding of linear and exponential functions, their applications, and how to graph them.
  
  Label: multiple-question