Final answer:
The function ƒ(x) = 1.25x best describes a scenario where the value of ƒ(x) is positive and increasing at a decreasing rate for increasing values of x.
Step-by-step explanation:
Of the given models, the function ƒ(x) = 1.25x best fits a scenario where the value of ƒ(x) is positive and increasing at a decreasing rate for increasing values of x. This linear function has a positive intercept, and since its slope is a constant positive value, it implies as x increases, so does ƒ(x), but the magnitude of the slope (rate of increase) does not decrease, it remains 1.25. This makes it better than ƒ(x) = 3(1.25)x which would increasingly grow at an increasing rate due to its exponential nature, and ƒ(x) = -3x - 3, which is a line with a negative slope, would decrease as x increases, contrary to the condition that ƒ(x) is positive and increasing. Lastly, ƒ(x) = 3x2 – 12x - 3 is a quadratic function with a positive coefficient for the x2 term which means its slope increases as x increases, which is again not fitting the condition of a decreasing rate of increase.