For the data set shown by the table,

a. Create a scatter plot for the data. (You do not need to submit the scatter plot)

b. Use the scatter plot to determine whether an exponential function or a logarithmic function is
the best choice for modeling the data.

Number of Homes Built in a Town by Year

years

1985
1991
1994
1997
2002

number of home

12
91
145
192
224

Amplitude: (8.19-3.91)= 4.28/2 = 2.14

y= 2.14*sin((pi/6)x-phi) +6.05
y = 2.14*sin((pi/6)(1) - phi) + 6.05 = 3.91

what do I do next? Please write out the steps.

To determine whether an exponential function or a logarithmic function is the best choice for modeling the data, you can follow these steps:

1. Plot the data points on a scatter plot, with the x-axis representing the years and the y-axis representing the number of homes built.

2. Once you have plotted the data points, observe the pattern that the points make on the graph.

3. Look for any common trends or patterns in the scatter plot. Specifically, pay attention to how the data points are distributed and whether they appear to follow a specific shape or curve.

4. For an exponential function, the data points would typically be grouped more closely together and form a curve that is increasing or decreasing rapidly.

5. For a logarithmic function, the data points would usually form a curve that increases or decreases slowly and then levels off at a certain point.

6. Examine whether the data points resemble an exponential curve or a logarithmic curve. Consider whether the trend appears to be exponential growth, exponential decay, logarithmic growth, or logarithmic decay.

7. Based on your analysis of the scatter plot, determine whether the data points are better fit by an exponential function or a logarithmic function. Consider factors such as the shape of the scatter plot, the overall trend, and the alignment of the data points.

In this particular case, based on the given data points, it is not clear from the information provided whether an exponential or logarithmic function is the best choice for modeling the data. It would be helpful to have more data points and additional information to make a more accurate determination.