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Solving Exponential Functions

Today you will need:

  1. Chromebook & Calculator
  2. Notes & pencil
  3. Positive Attitude :-)

Grab a warm-up from the wooden desk and get started!

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Goals:

  • Investigate solutions to exponential functions by graphing.
  • Solve exponential functions using equivalent expressions.

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Warm-up #1

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Warm-up #2

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Log on to Student.Desmos.com

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Solving Exponential Functions

Today you will need:

  • Chromebook & Calculator
  • Notes & pencil
  • Positive Attitude :-)

Grab a warm-up from the wooden desk and get started!

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Goals:

  • Investigate solutions to exponential functions by graphing.
  • Solve exponential functions using equivalent expressions.

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Warm-up #1

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Warm-up #2

Two freight trains are traveling to Columbus, Ohio. A graph is shown representing each train’s remaining distance to Columbus over time.

  1. Compare the distances relative to Columbus from which the trains begin their trip.

  • Tom claims both trains traveled at the same speed over a certain interval. Sara claims that both trains traveled at different speeds the entire time. Justify which claim is correct.

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Solving exponential equations using algebra

Can you solve each of these equations for x?

What strategies did you use?

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The Exponent Property of Equality:

Two powers with the same positive _______, b, are ____________ if and only if their exponents are equal.

For example: If 2x=25, then x=5.

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Solving exponential equations using algebra

Can you solve each of these equations for x?

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Solving exponential equations using algebra

Can you solve each of these equations for x?

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Skipped Desmos?

Check out this alternate way to solve any equation!

Method 1

Method 2

Method 2: Graphed

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Skipped Desmos?

Check out this alternate way to solve any equation!

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Skipped Desmos?

Check out this alternate way to solve any equation!

1.) Is it possible for an exponential equation to have no solution? More than one solution? Explain your reasoning.

2.) How can you solve an exponential equation graphically?

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Log on to Student.Desmos.com

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Toss the Squish!

Today I learned... relating to exponential functions.

One question I still have is...

I know that I need to work more on...

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Independent Practice: Delta Math

A15: Exponential Functions

Skills

Youtube Links

Exponential Rules (Level 1)

Negative Exponents Timed (Level 1)

Simplifying Radicals (Guided)

Simplifying Radicals

Basic Radical Operations

Multiply/Divide Radical Expressions

Adding/Subtracting Radical Expressions

Exponential and Radical Form

Exponential Functions - Basic

Nth Term of a Geometric Sequence

Table to Exponential Function

Exponential from Two Points (Level 1)

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Resources

  • Warm-up from Algebra by Example
  • Notes adapted from Big Ideas 6.5

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Mod 6 Standards

http://education.ohio.gov/getattachment/Topics/Learning-in-Ohio/Mathematics/Ohio-s-Learning-Standards-in-Mathematics/ALGEBRA-1-Standards.pdf.aspx?lang=en-US

�A.SSE.3 Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.�C. Use the properties of exponents to transform expressions for exponential functions. For example 8^t can be written as 2^3t.

A.CED.1 Create equations and inequalities in one variable and use them to solve problems. Include equations and inequalities arising from linear, quadratic, simple rational, and exponential functions.�a. Focus on applying linear and simple exponential expressions.

A.CED.2 Create equations in two or more variables to represent relationships between quantities graph equations on coordinate axes with labels and scales.�a. Focus on applying linear and simple exponential expressions.

F.LE.1 Distinguish between situations that can be modeled with linear functions and with exponential functions.�c. Recognize situations in which a quantity grows or decays by a constant percent rate per unit interval relative to another.

F.LE.2 Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table).

F.LE.5 Interpret the parameters in a linear or exponential function in terms of a context.

F.BF.1 Write a function the describes a relationship between two quantities. a. Determine an explicit expression, a recursive process, or steps for calculation from context. i. Focus on linear and exponential functions.

F.IF.9 Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). For example, given a graph of one quadratic function and an algebraic expression for another, say which has the larger maximum.�b. Focus on linear, quadratic, and exponential functions.

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Use a graphing calculator to solve the exponential equation given. Describe your process and explain how you determined the solution.

Questions to consider: What is the input? What is the output? How can I use the graphing function in my TI-84?

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Exploration #2: TYPES OF SOLUTIONS

Graph the given exponential function.

Can you graph a linear equation that will never intersect the exponential function?

Can you graph a linear function that will intersect the graph in more than one point?

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Use a graphing calculator to solve each equation graphically.

How can you solve an exponential equation graphically?