c). x 0 1 2 3 y 3 4.5 6.75 10.125

Notice that as each x increases by 1, each y does NOT increase by a constant amount. Thus, the data cannot be modeled by a linear function. Since the ratio of consecutive y-values is 1.5 , the model will be exponential. There are two ways to obtain an exponential model for this data: symbolically and by the calculator using exponential regression.

1). Finding the model symbolically.

The general form of an exponential is . Recall that C is the value of the function when x = 0.
Since the data point (0, 3) is given, C = 3 and since every y-value is 1.5 times the previous value, a = 1.5.

Therefore, the exponential function which models the data is .

2). The equation of the curve can be determined using the calculator exponention regression capability as follows:
Press STAT then select EDIT. Enter the x values in and the y values in . Check the menu to be sure that there are no functions listed and Plot1 is on (highlighted). Set the Viewing Rectangle to [-10,10,1] by [-10,20,1]. Then press GRAPH to see the scatterplot of the data. Note that the points do not appear to be in a straight line.

 

Next press STAT, ARROW RIGHT to CALC, the select 0:ExpReg. Then press ENTER.

The results show that the equation form is y= a* b^x (same as ), where a=3 and b= 1.5. Thus, the result is y = 3*(1.5)^x which is identical to . To verify this graphically, graph the function, and the scatterplot simultaneously. The result is shown below.

Therefore, the exponential function which models the data is .