Exponential Functions

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• • Investigating exponent rules

    • Write 64 in as many ways as possible using exponent notation. For instance 32*2 = 2^5*2^1 or 16*4=2^4*2^2 or 2*2*2*2*2*2=2^6 etc. As we know that these must all be the same number then we can see that 2^a*2^b=2^(a+b).

    • You can come up with the rule that a^c*b^c=(a*b)^c by coming up with the factorizations of 225 for instance.

    • You can also have students conjecture rules first and then use factorizations like these to check which rules work.

  • IBL Calculus linear and exponential exploration which helps students develop a characterization of liner and exponential growth: https://sites.google.com/site/aibldraftinstructorsite/home/in-class-activities-and-activity-guides/ca-i4-linear-and-exponential-characteristics

  • IBLCalculus Precalculus page contains a whole section on Exponential functions with a variety of activities: https://sites.google.com/site/aibldraftinstructorsite/precalculus

  • Use www.desmos.com to compare power functions and exponential functions. Have students graph 2^x and x^2 from 0 to infinity. When is 2^x bigger? When is x^2 bigger? In the long run which function is bigger? Do the same thing with 3^x and x^3?

  • Make table for (-2)^x. Notice in this Desmos graph that Desmos will graph the table of (-2)^x but not the form f(x)=(-2)^x - why is this? Is this a function? What is the domain? What is the range? https://www.desmos.com/calculator/iqyqr27hhu

  • Desmos Activities: https://teacher.desmos.com/exponential