7-1 Exploring Exponential Models

Objective

To model exponential growth and decay

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The number of moves needed for additional rings in the Solve It suggests a pattern that approximates repeated multiplication.

Essential Understanding You can represent repeated multiplication with a function of the form y = a b x y equals eh , b to the x  where b is a positive number other than 1.

An exponential function is a function with the general form y = a b x , y equals eh , b to the x , comma   a ≠ 0 , eh not equal to 0 comma  with b > 0 , b greater than 0 comma  and b ≠ 1 . b not equal to 1 .  In an exponential function, the base b is a constant. The exponent x is the independent variable with domain the set of real numbers.

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