The function that best fits the points (0, 3), (1, 6), (2, 12), (3, 24) is an exponential function, specifically y = 3 * 2^x.
To determine the function that best fits the given points (0, 3), (1, 6), (2, 12), (3, 24), we can analyze the relationship between the x-values (independent variable) and the y-values (dependent variable) by plotting the points and examining the pattern of the data.
When plotted on a graph, it can be seen that as x increases, y is not increasing by the same amount each time, which eliminates a linear relationship. Instead, for each increase in x, the value of y doubles, which is characteristic of an exponential function.
Unlike a quadratic function, where the rate of change of y would increase by an additional constant amount with each increase in x, the rate of change here is multiplicative.
Therefore, an exponential function of the form y = ab^x appears to be the best fit for the data, with the base b being 2 since the y-values double when x increases by 1, starting from y=3 when x=0. This suggests the function that best fits the given points is y = 3 * 2^x.