Exploring Exponential & Logarithmic Functions
[b]Explore Exponential and Logarithmic Functions [/b][color=#b20ea8][/color]
Table of Contents
- Logarithm and Exponential functions
- Exponential Functions: Graphs
- Logarithmic Functions: Graphs
- Half-Life Action!!!
- Half-Life Action (3)!!!
- Half-Life Action (2)!!!
- Logarithmic function properties
- Logarithmic Action (1)!
- Logarithmic Action (2)!
- Logarithmic Action (3)!
- Logarithmic Action (4) or (3, V2)!
- Logarithmic Action(5)!
- Applications
- Compound Interest Investigation: Earning Money
- Comparing Compounding Interest Formula-continuously
- Compound interest and exponential functions
- 7.1 Graph Exponential Growth Functions
- Laws of Logarithms
Exponential Functions: Graphs
The following applet displays the graph of the exponential function [math]f\left(x\right)=c\cdot a^{kx}+d[/math]. [br]Interact with the applet below for a few minutes, then answer the questions that follow.
[b][color=#000000]Questions:[/color][/b][br][br][color=#000000]1) How does the parameter [/color][color=#cc0000][b]a[/b][/color] [color=#000000]affect the graph of the exponential function? Explain. [br] What happens if [/color][color=#cc0000][b]a > 1[/b][/color][color=#000000] and [/color][color=#1e84cc][b]k > 0[/b][/color][color=#000000]? What happens if [/color][color=#cc0000][b]a < 1[/b][/color][color=#000000] and [/color][color=#1e84cc][b]k > 0[/b][/color][color=#000000]? [br][br][/color][color=#000000]2) How does the parameter [/color][b][color=#1e84cc]k[/color][/b][color=#000000] affect the graph? Explain. [br] If you need a hint, refer back to [url=https://www.geogebra.org/m/HJvZSUna]this worksheet[/url]. [br][br][/color][color=#000000]3) What does the parameter [/color][color=#980000][b]d[/b][/color][color=#000000] do the graph? Explain. [br][br][/color][color=#000000]4) Suppose [/color][color=#cc0000][b]a < 1[/b][/color][color=#000000]. [br] Given this constraint, is it possible to get the graph of this exponential function to look the way it does[br] when [/color][color=#cc0000][b]a > 1[/b][/color][color=#000000] and [/color][color=#1e84cc][b]k > 0[/b][/color][color=#000000]? Explain. [/color]
Logarithmic Action (1)!
Interact with the applet below for a few minutes.[br]. [br]Prior to starting, feel free to move the [b][color=#980000]brown[/color][/b] and [color=#9900ff][b]purple[/b][/color] point wherever you'd like (on the x-axis.) [br]You can move the [b][color=#38761d]green point[/color][/b] anywhere you'd like as well. [br][br][b]Note:[/b][br]In order to see the [b]referenced black point[/b] that eventually appears, [b]you may need to zoom out[/b] a bit. [br]
[b]In general, how can you express the sum of two logarithms as the logarithm of a single quantity? [/b]
Compound Interest Investigation: Earning Money
[b]Students: [/b][br][br]Use this applet to help you research answers to the questions posed in the[br][i][color=#0000ff][b]Compound Interest Investigation: Earning Money[/b][/color][/i] investigation you received at the beginning of class.