Chapter 5.9, Problem 5AYU

Milk Production The data in the table below represents the number of dairy farm ( in thousands) and the amount of milk produced ( in billions of pounds) in the United States for various years.

$\begin{array}{ccc}\begin{array}{l}\\ \text{Year}\end{array}& \begin{array}{l}\text{Dairy}\text{Farms}\\ \text{(thousands)}\end{array}& \begin{array}{l}\text{Milk}\text{Produced}\\ \text{(billion}\text{pounds)}\end{array}\\ 1980& 334& 128\\ 1985& 269& 143\\ 1990& 193& 148\\ 1995& 140& 155\\ 2000& 105& 167\\ 2005& 78& 177\\ 2010& 63& 193\\ 2015& 44& 209\end{array}$

Source: National Agricultural Statistics Services

Using a graphing utility, draw a scatter plot of the data with the number of dairy farms as the independent variable.

Using a graphing utility, build a logarithmic model from the data.

Graph the logarithmic function found in part (b) on the scatter plot.

In $2008$, there were $67$ thousand dairy farms in the United States. Use the function in part (b) to predict the amount of milk produced in $2008$.

The actual amount of milk produced in $2008$ was $190$ billion pounds. How does your prediction in part (d) compare to this?