Final answer:
The question aims to find an exponential model for the provided data, but the correct model format should be y = ab^x or y = ae^bx. The format y = ax + b is for a linear model and doesn't fit exponential data. To choose an appropriate model from the options, exponential regression analysis must be performed with technology support.
Step-by-step explanation:
To find an exponential model for the given data set, one would need to use regression analysis to determine the parameters for the model that best fits the data. Unfortunately, the given format provided in the question (y = ax + b) suggests a linear model which is incorrect for fitting exponential data. The correct model format should be y = abx or y = aebx, where e is the base of the natural logarithm approximately equal to 2.71828.
Considering the options provided (A, B, C, and D), they all express exponential growth as expected, but differ in their base and exponent parameters. Calculating the exponential model accurately requires the use of technology, such as a graphing calculator or statistics software that can perform exponential regression. Each option can be evaluated by inserting the x-values into the equations and comparing the resultant y-values with the given y-data. The model with the smallest residuals (the differences between the actual y-values and the values predicted by the model) is the best fit.
Neither the question nor the provided examples offer sufficient information to directly calculate the exponential model, so no definitive answer to the selection of A, B, C, or D can be provided without additional computation.