unit 2 exponential & logarithmic functions
"Power Rule"
(Lyrics by Coulliette, King, & Rosas-Guyon Tune - "When You’re Happy”) When you multiply like bases, add exponents. When you divide like bases, Subtract exponents. With a power to a power, With a power to a power, With a power to a power, Muliply. When you have a negative exponent Change it’s place; Reciprocate! When you have zero exponent you get one. When you learn these rules, When you learn these rules, When you learn these rules, Then you can pass. Log Base Change Property
[Emily Hudspeth ’07 Covenant High School] Tune: Silent Night Log base b of x is log base a of x all over log base a of b this is the general equation for the change of base property for all the different logs now go pass your test. "Exponents 2"
Tune: "Jingle Bells" Exponents, Exponents, Powerful things! Raise you up, and root you down, are what logarithms bring. Natural is e, Common is 10, e to the zero's one, 10 to the zero's one again! To multiply just add, To divide simply subtract, But be sure your bases match or you're on the wrong track! Oh, Exponents, Exponents, Powerful things! Raise you up, and root you down, are what logarithms bring. |
Exponentials
Tune – “Head and Shoulders” (My Godson Marcellus was the inspiration for this song.) Exponential Equations – Y equals A times B to the x. – X up high, and not down below. That’s the Exponential Equation. A is for the beginning amount. - B is 1 plus or minus the rate. X up high, and watch the time go by. That’s the Exponential Equation. The Number We Call “e”
Tune – “The Lion Sleeps Tonight” by John A Carter – Chicago, IL Chorus e-e-e-e- e-e-e-e-e- 2 point 7-1-8 2-7-1-8 (10 times) There’s a number A special number We use it constant-leeee (2 times) Chorus For log-a-rithms Yes log-a-rithms The base is naturally-eeee (2 times) Chorus To com-pound int’rest Contin-u-ous int’rest It’s Pert shampoo for meeeeeee (2 times) Chorus (Two parts) Part 1 – e-e-e-e-e-e-e-e-e-e,2 point 7-1-8 Part 2 – 2-7-1-8,…2-7-1-8,…2-7-1-8 "Systems"
Lyrics & Performance by Vicki Young Melody “Your are My Sunshine” The other day, dear, As I was graphing. Instead of one line there were 2. I was perplexed until I realized. My teacher would tell me what to do. When you have two lines, It’s called a system, And there are three outcomes you will view. They’re parallel lines or they’re the same line, Or they cross in one point that is true. |
"Scientific Notation"
(new lyrics by Jill Nielsen
Tune - "Pop Goes The Weasel")
To Change to scientific notation
The decimal you place first.
The absolute value less than 10
But greater than or equal to one.
How many places must you move
The original decimal to get there?
Count them up and make it the power of 10
Exponent rising like a star.
Which direction did you go
When you moved the decimal?
Left makes it neg. and right makes positive
Powers for the 10 that’s all.
Now you can place a great bit X
Between the number and 10’s powers.
The X means multiplication here
From scientific notation don’t cower.
(Chorus)
Scientific Notation
We change to it.
When we use these basic steps.
It’s an easy trip.
(new lyrics by Jill Nielsen
Tune - "Pop Goes The Weasel")
To Change to scientific notation
The decimal you place first.
The absolute value less than 10
But greater than or equal to one.
How many places must you move
The original decimal to get there?
Count them up and make it the power of 10
Exponent rising like a star.
Which direction did you go
When you moved the decimal?
Left makes it neg. and right makes positive
Powers for the 10 that’s all.
Now you can place a great bit X
Between the number and 10’s powers.
The X means multiplication here
From scientific notation don’t cower.
(Chorus)
Scientific Notation
We change to it.
When we use these basic steps.
It’s an easy trip.