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?
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.
Sample Response: If the base of the exponent were 1, the function would remain constant. The graph would be a horizontal line. If the base of the exponent were less than 1, but greater than 0, the function would be decreasing.
