Final answer:
Equations I, II, and III are exponential functions because they have constants raised to a variable power. Equation IV is also an exponential function with a subtraction and does not fit the form of a linear equation.
Step-by-step explanation:
To determine which equations are possible solutions, we need to first understand the nature of exponential functions and linear equations. Exponential functions have the form y = a^x, where 'a' is a constant and 'x' is the exponent. Linear equations are of the form y = mx + b, where 'm' is the slope and 'b' is the y-intercept.
Analyzing the given equations:
I. y = 1/2(3)^x is an exponential function because it has a constant base of 3.
II. y = 3(1/3)^x simplifies to y = 3 × 3^(-x), which is also an exponential function with a constant base of 3.
III. y = (1/2)^(x+2) is an exponential function as it has a constant base of 1/2.
IV. y = 2^x - 1 can be mistaken for a linear function, but it's an exponential function with 1 subtracted from it; hence, it does not fit the linear equation form.
Based on this analysis, the possible solutions that are exponential functions are I, II, and III. However, IV is also an exponential function, just modified by a subtraction, so it might fit depending on the context of the original question which had typos and irrelevant parts removed.