in exponential growth functions, the base of the exponent must be greater than 1. how would the function…

Explanation:

Step1: Analyze base = 1 case

Let the exponential - function be (y = a\cdot b^x), where (a\neq0) and (b) is the base. When (b = 1), then (y=a\cdot1^x). Since (1^x = 1) for all real - valued (x), the function becomes (y=a), which is a constant function. It does not grow or decay; the output value remains the same regardless of the input (x).

Step2: Analyze base between 0 and 1 case

When (0 < b<1), the function (y = a\cdot b^x) is an exponential decay function. As (x) increases, the value of (b^x) gets smaller. For example, if (b=\frac{1}{2}) and (x = 1), (y=a\cdot\frac{1}{2}); if (x = 2), (y=a\cdot(\frac{1}{2})^2=a\cdot\frac{1}{4}); if (x = 3), (y=a\cdot(\frac{1}{2})^3=a\cdot\frac{1}{8}). The function values decrease as (x) increases.

Answer:

If the base of the exponent were 1, the function would be a constant function (y = a) (where (a) is the coefficient of the exponential term). If the base of the exponent were between 0 and 1, the function would be an exponential decay function, and the function values would decrease as (x) increases.