5 – Exponential Functions

Skills to Master

  • Rules (Laws) of Exponents
  • Writing Exponential Functions
    • A.CED.1 – Create equations in one variable and use them to solve problems.
  • Create Tables & Graphs of Exponential Functions (from Scenarios)
    • F.LE.2 – Construction of Exponential Functions, Graphs, scenarios, & a table.
    • F.IF.7e – Graph exponential functions.
  • Interpret Key Features of Exponential Functions
    • F.IF.4 – Interpret key characteristics of exponential functions.

Video Tutorials

Video # 1 – Writing Exponential Functions from a Table

IM1 – Writing #Exponential Functions from a #Table

Video # 2 – Graphing Exponential Functions & Identifying Key Characteristics

IM1 – #Graphing #Exponential Functions & Identifying #Key Characteristics

Video # 3 – Writing Exponential Functions from Growth & Decay Scenarios

  • Base, b: The BASE represents EVERYTHING you have, 100% of it, PLUS or MINUS the Growth or Decay RATE
  • Shortcut Formula for Rewriting a Rate, r, % as a Decimal for the base, b:
    • Growth: b = 100 + r % (then move the decimal two places to the left)
    • Decay: b = 100 – r % (then move the decimal two places to the left)
  • For THESE scenarios (in video # 3), practice calculating time based on ONE YEAR. Divide up one year into days, weeks, months, hours, seconds, etc. See examples…
    • Days: t / 365
    • Weeks: t / 52
    • Months: t / 12
    • Hours: t / 8760……. because 365 days times 24 hours
    • Minutes: t / 525600……. because 365 days times 24 hours times 60 minutes
#Exponential #Functions #Growth #Decay

Video # 4 – Determining Growth or Decay from the Base of an Exponential Function

  • b: base (written as a fraction or decimal)
    • Growth: b > 1
    • Decay: 0 < b < 1
#growth #decay #base #exponential #function

Video # 5 – Calculating Percent Rate of Change

  • Symbols
    • r: Rate of Change (in %)
    • b: base
    • %: Percent
  • Step 1: Convert the base.
    • a) Rewrite all fractions as decimals.
    • b) Then, rewrite all decimals as percents (multiply by 100 or move the decimal 2 places to the right and use % sign). This gives you the base, b %.
  • Step 2: Identify if the function represents growth or decay
    • Growth: 100 % + rate % = base %
      • Solve for the Growth rate, r (r % = b % – 100 %)
    • Decay: 100 % – rate % = base %
      • Solve for the rate of Decay, r (r % = 100 % – b %)
#percent #rate #calculate #percentrateofchange #percentrate #exponential #function #base

Video # 6 – Exponential Function (Scenario Walk-Thru for Problem # 1 of 5.3 ev2)

  • Exponential Function Form: f(x) = a ⋅ bx
  • Exponential Function Form (based on TIME, t): f(t) = a ⋅ bt
  • Symbols
    • a: initial (starting) value
    • r: rate of growth or decay
    • t: time
      • For THESE scenarios (videos # 6 & 7) , do NOT break up time based on one year.
      • Time will be represented in countable increments, consecutively.
      • You will count how many hours, minutes, days, years from or before the starting time, “right now.” Ex. If t = 6: 6 hours from now. Ex. If t = -3: 3 hours ago.
      • Time, t, represents the exponent, but you can also use x.
Exponential Function (Scenario Walk-Thru of Practice 5.3 eV2)

Practice Worksheet for Videos # 6 & 7

  • Watch video # 6 and work through Problem # 1 (Pages 1 & 2) of this worksheet while watching & pausing.
  • Then, try Problem # 2 (Page 3) of this worksheet, then watch video # 7 to check your work!
IM1-5.3-P-eV2-Creating-Exponential-Functions-Given-Scenarios

Video # 7 – Exponential Function (Scenario Walk-Thru for Problem # 2 of Practice 5.3 eV2)