Exponents & LogsStarting with Log

What do we know about 9^2?

(a)That it is the same as 81(b)That it is the same as 3^4(c)That its absolute value is bigger than 9^-7(d)That there could be a number where 5^number = 9^2

What do we know about 3^1.5?

(a)That it is 3 times itself one and one-half times(b)That it has no real meaning(c)That 3^1.5 * 3^1.5 =‘s 3^3 or 27(d)Is greater that 3^-7

Non-dichotomous Multiple Choice

Hmm …

Let’s see if we can find 3^? = 8 using a calculator(we know it will be between 3^1 and 3^2, why?

Try 3^ ____ is ____

Try 3^ ____ is _____

Using base 3, find the exponents for 3^? for two numbers that you choose

First Number

2ndNumber

See how close you can get?

Now multiply these numbers If we write it as 3^__ * 3^___ then thisShould be the same as3^(__ + __)Try it…

Start with same numbers but different base … repeat

Hard way …. Guess and check

This is what Log does

What power do we raise the base to To get ____

Logbase

____

Re-write your quests in terms of logs

Try on calc

Multiply by adding these results on calc

Nice!

Things that grow exponentially – Times 10 …

Log of things that grow exponentially (are straight)

M&M’s etc.

Stations

Is exp?

How know?

Get two different graphs(by changing ___)

What is the proportion of Growth/Decay:?

Report out …

Think of 1 during movieOne growth but not exp

Table of Step Number Log (N)

http://generative.edb.utexas.edu/materials/exponents_stations/exponent_stations.html

http://generative.edb.utexas.edu/materials/exponents_stations/exponent_stations.html

Before Disease …

N^x (increasing or decreasing multiplicatively … not additively]

>See next slide < Formative assessment [fill out table] – what do you think for each … then vote … then discuss or just play ..

Exponential?

Increasing Decreasing?

Then connect to disease (exponential? Increasing decreasing? Where? Why?

Then to

More notes: Could have introduce and describe scenario and aske students if to fill out table.

Scenario Exponential?

Increasing/decreasing?

Shape of graph

01 M&M Losing Blues

02 R-decay

03 Credit Card Debt

Others.

Prior to DiseaseOr for other groups to replace buzz bugs … or skittles…

or other

or other

or other

or other