# 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