# Problem 414

Students  Per Computer

In the early years of microcomputers, school districts could not afford to buy a computer for every student. As the price of computers decreased, more and more school districts have been able to attainthis goal. The following table lists numbers of students per computer during these early years.

 Year 1983 1985 1987 1989 Students/Computer 125 50 32 22

 Year 1991 1993 1995 1997 Students/Computer 18 14 10 6

(a)    Make a scatterplot of the data. Would a straight line model the data accurately? Explain.

(b)   Discuss how well the formula

S = , y ≥ 1983

models these data, where S represents the students per computer and y represents the year.

(c)    In what year dose the formula reveal that there were about 17 students per computer?

Solution Form the above graph we can see that we can’t join all points with straight line, so we can’t use any straight line model.

B.

when y = 1983

S = Plug in y = 1983 in the given formula

S =  S = 125

When y = 1985

S = S = S = S = S = 52

When y = 1987

S = S = S = S = S = 33

When y = 1989

S = S = S = S = S = 24

When y = 1991

S = S = S = S = S = 19

When y = 1991

S = S = S = S = S = 16

All calculated data’s are not same as the given table so we can say that given formula is not accurate for the given data.

C.

17 students per computer

Given value is S = 17, now plus in this value in the given formula

17 = 17(1 + 0.7 (y – 1983)) = 125

17(1 + 0.7y -1388.1) =125

17(0.7y – 1387.1) =125

11.9y -23580.7 = 125

11.9y = 125 + 23580.7

11.9y = 23705.7

Y = Y = 1992

So in the year of 1992 there are 17 students per computer.