14. (a) Use a graphing utility to find the exponential regression function for the follow data:
{(23.5, 16), (26.7, 48), (28.0, 155), (29.5, 571), (29.9, 896)}
To find the exponential regression function for the given data, you can use a graphing utility software like Excel or online tools such as Desmos or Wolfram Alpha. Here's how you can do it using Desmos:
1. Go to the Desmos website (https://www.desmos.com/) and open the graphing calculator.
2. Enter the given data points in the form of (x, y) pairs into separate columns. For example, enter the x-values in column A and the corresponding y-values in column B.
3. In the graphing calculator, click on the "+" button in the top-left corner of the screen to add a new expression.
4. In the expression bar, type "y1~a*b^x" to define the exponential regression function, where 'a' and 'b' are unknown coefficients.
5. Press the enter key, and you will see that Desmos automatically adds sliders for 'a' and 'b' to the left of the graph.
6. To fit the regression line to the data, you need to adjust the sliders manually. Click on the sliders and drag them until the regression line best fits the given data points.
7. Once you have found the best-fit regression line, you will be able to read off the exponential regression equation in the form of "y = a * b^x." The values of 'a' and 'b' will depend on the specific data set.
Using this method, you can find the exponential regression function for the given data, {(23.5, 16), (26.7, 48), (28.0, 155), (29.5, 571), (29.9, 896)}.