Explaining Exponential Growth in Terms of the Base of the Exponent In exponential growth functions, the base of the exponent must be greater than 1. How would the function change if the base of the exponent were 1? How would the function change if the base of the exponent were between 0 and 1?

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Mathematics

Jaylah Bentley

8 July, 05:41

Explaining Exponential Growth in Terms of the Base of the Exponent In exponential growth functions, the base of the exponent must be greater than 1. How would the function change if the base of the exponent were 1? How would the function change if the base of the exponent were between 0 and 1?

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Barbara Norman · Answer 1

Take an example y = 2^x The exponent is x.

when x = 1,2 and 3 y will be 2^1 = 2, 2^2 = 4 and 2^3 = 8

So the values of y grow very rapidly with base 2.

They would grow even more rapidly with higher bases.

if the base = 1 there would be no growth because 1 to any exponent still = 1.

1^2 = 1, 1^1000 = 1 and so on.