In an economics class, students were given a final exam at the end of the course. Then they were retested with an equivalent test at subsequent time intervals. Their scores after time x, in months, are listed in the table below.
Time, x (in months) Score, y
1 .............................. 84.9%
2 ................................. 84.6
3 ................................. 84.4
4 ................................. 84.2
5 ................................. 84.1
6 ................................. 83.9
a) Use a graphing calculator to fit a logarithmic function y = a + b ln x to the data.
b) Use the function to predict test scores after 8, 10, 24, and 36 months.
c) After how long will the test scores fall below 82%?