## pre-calculus 12 Exponential and Logarithmic Functions

**Specific Curriculum Outcomes**

**RF07**Demonstrate an understanding of logarithms.

**Note RF07.03 Includes the number e, Euler's number, and natural logarithms. This is part of the NS curriculum but not the WNCP Curriculum. There are no problems in the textbook relating to e or ln but there are a number of activities and problems in the curriculum guide.*

**RF08**Demonstrate an understanding of the product, quotient and power laws of logarithms.

**RF09**Graph and analyze exponential and logarithmic functions.

**RF10**Solve problems that involve exponential and logarithmic equations.

## RF07 activities

**Calculating e by Hand**- Pick a random number between 0 and 1. Repeat until the sum of the numbers picked is >1. On Average, this will take e picks. You can turn this into an investigation by rolling dice in a variety of ways.

**e (Euler's Number) video from Numberphile**- Dr James Grime discusses "e" - the famed Euler's Number.

## RF08 Activities

**Exponents & Logarithms the MTBoS way from John Rowe -**John describes a number of activities he uses to teach exponents and logarithms.

## RF09 Activities

**Folding Paper More than Seven Times from Mythbusters**- "A popular myth exists that one can only fold a single piece of paper in half, seven, maybe eight times at most. To squelch this popular myth, the folks over at Mythbusters did what any “rational” person might attempt; they produced an enormous sheet of paper, something roughly the size of a football field. Together with a team of their accomplices, a steam roller and a forklift, they successfully folded this enormous sheet eleven times." from Relatively Interesting. There are lots of great classroom activities using this idea.

**Exponentials Polygraph Activity from Desmos**- This Custom Polygraph is designed to spark vocabulary-rich conversations about exponentials, including how they differ from linear functions. Key vocabulary that may appear in student questions includes: increasing, decreasing, intercept, rate, asymptote, and curve.

**Marbleslides: Exponentials from Desmos**- In this delightful and challenging activity, students will transform exponential functions so that the marbles go through the stars. Students will test their ideas by launching the marbles, and have a chance to revise before trying the next challenge.

## RF10 Activities

**Plotting the Planets from Underground Maths**- In this resource, students use logarithms to explore real data, investigate relationships and produce modelling formulae.

**Creating a Need for Logarithms with Zombies from****Julie Reulbach**- Students are turning into Zombies at an exponential rate! How many hours until the entire student body is ALL Zombies? Solving this problem without logarithms will take some persistence and trial and error. Once students have a good idea of the solution, show them how to use logarithms to find the exact answer.