Explaining Exponential Growth in Terms of the Base of the Exponent In exponential growth functions, the base of the exponent mus
t 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.
