Chapter 3.4, Problem 36E

(a)

To determine

To calculate: The logarithm function $y=a+b\ln x$, using regression to fit the data provided below.

Time, $t$(in weeks)	1	2	3	4	5	6
Score, $y$	$84.9\text{\%}$	$84.6\text{\%}$	$84.4\text{\%}$	$84.2\text{\%}$	$84.1\text{\%}$	$83.9\text{\%}$

(b)

To determine

To calculate: The average test score after 8 weeks, 10 weeks, 24 weeks, and 36 weeks with the help of the function $y=84.94353992-0.5412834098\ln x$.

(c)

To determine

To calculate: The time when test scores fall below $82\%$, where the function $y=84.94353992-0.5412834098\ln t$ predicts the average test score after $t$ weeks.

(d)

To determine

To calculate: The rate of change of scores given by the function $y=84.94353992-0.5412834098\ln t$ and interpret its meaning.