Exponential function and Geometric progression

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Every exponential function can be represented as a geometric progression because it involves constant multiplicative growth. However, not all geometric progressions qualify as exponential functions since they may not have a constant ratio or may include non-exponential sequences. The analogy comparing humans to mammals illustrates that while all exponential functions fit within the broader category of geometric progressions, the reverse is not true. This distinction highlights the specific nature of exponential growth compared to the more general concept of geometric sequences. Understanding this relationship is crucial for grasping the properties and applications of these mathematical concepts.
schan11
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Can anyone help me answer this question?


" Every exponential function is a geometric progression but not every geometric progression is an exponential function. Explain."
 
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It would be nice if you had some ideas you tried but couldn't get to work in your head.

Think of it this way:
Every human is a mammal, but not all mammals are humans.

Basically, I just changed the objects, but the principle is the same. What does it imply if every human is a mammal? What does it imply if not all mammals are humans?
 

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