Skills to Master
- Rules (Laws) of Exponents
- Pre-Requisite
- Video
- Writing Exponential Functions
- A.CED.1 – Create equations in one variable and use them to solve problems.
- 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
Video # 2 – 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
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
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 %)
- Growth: 100 % + rate % = 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.
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!
Video # 7 – Exponential Function (Scenario Walk-Thru for Problem # 2 of Practice 5.3 eV2)