M39

Exponential Function

MathematicsGrade 12Grade 11Grade 10Grade 2Grade KGrade 1Grade 3Grade 5Grade 6Grade 7Grade 8Grade 9Grade 4

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DEFINITION:
a function whose value is a constant raised to the power of the argument, especially the function where the constant is e.

HOW TO:
Graph the function y = 2x + 1. This will look kinda like the function y = 2x, but each y-value will be 1 bigger than in that function

Everyday Use: Null

Lyrics

Excuse me class (exponential high)  

May I have your attention please  

Excuse me  

May I have your attention please (and bases low, bases low) 

I raise the base to the power that I wanted (that I wanted)  

Now they can’t tell me nothing (why?)  

Cause it’s the topic of discussion (yes sir) 

And that’s the exponential, exponential function (let’s go) 

 

First is an equation for you scholars 

A times B raised to the X power 

See we ain’t living off potential  

If you ever check our growth, you will see that its exponential 

If you’re looking for a pattern, you will see it never adds up 

I mean it’s a different bill when it stacks up 

Make sure you’re really getting this 

All of our friend should always be multiplicative (yes) 

And even if you settle on a graph  

We’ll never line up you should do the math 

Yea, we’ll start of slow  

But we’ll shoot up right off go 

So, you should check us out 

I mean it graph goes sky high 

You can even wave it bye-bye 

So, there’s no need assumptions  

Cause you know now what’s exponential functions (let’s go) 

 

 

I raise the base to the power that I wanted (that I wanted)  

Now they can’t tell me nothing (why)  

Cause it’s the topic of discussion (yes sir) 

And that’s the exponential, exponential function (let’s go) 

 

I raise the base to the power that I wanted (that I wanted)  

Now they can’t tell me nothing (why?)  

Cause it’s the topic of discussion (yes sir) 

And that’s the exponential, exponential function (let’s go) 

Standards

  • CCSS.MATH.CONTENT.HSF.LE.A.1.A — Prove that linear functions grow by equal differences over equal intervals, and that exponential functions grow by equal factors over equal intervals.
  • CCSS.MATH.CONTENT.HSF.LE.A.1.C — Recognize situations in which a quantity grows or decays by a constant percent rate per unit interval relative to another.
  • CCSS.MATH.CONTENT.HSF.LE.A.1 — Distinguish between situations that can be modeled with linear functions and with exponential functions.
  • CCSS.MATH.CONTENT.HSF.LE.A.1.B — Recognize situations in which one quantity changes at a constant rate per unit interval relative to another.
  • CCSS.MATH.CONTENT.HSF.LE.A.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).
  • CCSS.MATH.CONTENT.HSF.LE.A.3 — Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as a polynomial function.
  • CCSS.MATH.CONTENT.HSF.LE.B.5 — Interpret the parameters in a linear or exponential function in terms of a context.
  • CCSS.MATH.CONTENT.HSF.LE.A.4 — For exponential models, express as a logarithm the solution to abct = d where a, c, and d are numbers and the base b is 2, 10, or e; evaluate the logarithm using technology.