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
well, I can not graph it very well but if exponential then
y = Ae^kx
x = year - 1985
12 = A e^0 = A(1) = A
so y = 12 e^kx
in 1994, x = 9 years
y = 12 e^9k = 145
e^9k = 145/12 = 12
9 k = ln 12 = 2.48
k = .276
now in 2002 we would get
x = 17
then we would get
y = 12 e^(17*.276)
y = 12 e^4.69
y = 1311 whoops, the data shows 224
not much of a fit
now try
ln fit and see if it is better
You can do the rest here , Thank you by the way !
a. To create a scatter plot for the given data set, plot the years on the x-axis and the number of homes built on the y-axis. Place a point on the graph for each data pair:
(1985, 12)
(1991, 91)
(1994, 145)
(1997, 192)
(2002, 224)
b. Upon examining the scatter plot, we can see that the points seem to be increasing rapidly at first and then starting to level off. This suggests that an exponential function might be the best choice for modeling the data. An exponential function is characterized by rapid initial growth that eventually slows down.
To create a scatter plot for the given data set, you need to plot the number of homes built on the y-axis and the corresponding years on the x-axis.
Here's how to create a scatter plot using this data:
1. Plot the years on the x-axis and the number of homes built on the y-axis.
- On the x-axis, mark the years 1985, 1991, 1994, 1997, and 2002.
- On the y-axis, mark the numbers 12, 91, 145, 192, and 224.
2. Plot the data points on the graph.
- Find the point of intersection for each year and the corresponding number of homes built.
- Mark the points on the graph accordingly.
3. Connect the data points.
- Draw a line or curve that passes through the plotted points to indicate the trend in the data.
Now that you have the scatter plot, you can use it to determine whether an exponential function or a logarithmic function is the best choice for modeling the data.
Both exponential and logarithmic functions can be used to describe growth and decay phenomena. To determine which function is the best fit for the data, you need to look at the scatter plot.
If the data points form a curve that increases or decreases rapidly at first but then starts to level off, an exponential function is a better choice. An exponential function is characterized by rapid growth or decay at the beginning and then approaches a limiting value.
Alternatively, if the data points form a curve that starts with rapid growth or decay but then levels off or slows down, a logarithmic function is a better choice. A logarithmic function shows rapid growth or decay initially but gradually slows down over time.
Based on the scatter plot, analyze the pattern of the points and determine whether they exhibit exponential growth or decay or logarithmic growth or decay.