Chapter 4.5, Problem 83E

(a)

To determine

To calculate: The logarithmic model for the average score s with respect to time t in months in an exam of learning theory study students which is retested in every six months and the table shows the average score s at various months t after the initial exam for the students using graphing utility.

t	$1$	$2$	$3$	$4$	$5$	$6$
s	$84.2$	$78.4$	$72.1$	$68.5$	$67.1$	$65.3$

(b)

To determine

To graph: The sketch of logarithmic model for the average score s with respect to time t in months with the help of provided table and by using graphical utility.

t	$1$	$2$	$3$	$4$	$5$	$6$
s	$84.2$	$78.4$	$72.1$	$68.5$	$67.1$	$65.3$

(c)

To determine

To calculate: The rate of change of s with respect to time t when $t=2\text{ and }t=5$ if s is the average score with respect to time t in months with the help of provided table,

t	$1$	$2$	$3$	$4$	$5$	$6$
s	$84.2$	$78.4$	$72.1$	$68.5$	$67.1$	$65.3$

(d)

To determine

The meaning of rate of change of s with respect to time t when $t=2\text{ and }t=5$ if s is the average score with respect to time t in months with the help of provided table,

t	$1$	$2$	$3$	$4$	$5$	$6$
s	$84.2$	$78.4$	$72.1$	$68.5$	$67.1$	$65.3$