Now lets do it using the geometric method that is repeated multiplication, in this case we start with x goes from 0 to 5 and our sequence goes like this: 1, 2, 2 2=4, 2 2 2=8, 2 2 2 2=16, 2 2 2 2 2=32. The conflicts have made me more confused about the concept of a dfference between Geometric and exponential growth.
21 It might help to think of multiplication of real numbers in a more geometric fashion. $2$ times $3$ is the length of the interval you get starting with an interval of length $3$ and then stretching the line by a factor of $2$. For dot product, in addition to this stretching idea, you need another geometric idea, namely projection.
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