The table below contains data on the total fall enrollment in degree-granting in
ID: 3000477 • Letter: T
Question
The table below contains data on the total fall enrollment in degree-granting institutions of higher education for selected years, 1970 through 2005.What is the change for the above data from the year 1970 to 2000? (Show work for partial credit.)
Interpret this description of change.
Year: 1970 1975 1980 1985 1990 1995 2000 2001 2002 2003 2004 2005
Enrollment: 8581 11185 12097 12247 13819 14262 15312 15928 16612 16911 17272 17487
a) What is the percentage change for the above data from the year 1970 to 2000? Interpret this description of change.
b)What is the average rate of change for the above data from the year 1970 to 2000?
Interpret this description of change
c)Find a cubic model for the total fall enrollment as a function of the number of years after 1970. Use two decimal place rounding and be sure to include all parts of a model.
d)Write the derivative of the model found in the cubic model.
Use it to determine the rate of change of total fall enrollment in the year 1990.
e) Find the percentage rate of change of total fall enrollment in the year 1990.
Explanation / Answer
(a)
% change = [(15312-8581)/8581]*100 = 78.44 %
this means that enrollment in 2000 increased by 78.44% as compared to enrollment in 1970.
(b)
assuming compounded change in number of enrollments for 30 years
let the rate of change be R
15312 = 8581(1+(R/100))^30
solving R = 1.95%
assuming simple rate change
average rate of change = (78.44/30) = 2.61%
(choose the answer that suits you best)
this means that the number of enrollments on an average grew by 1.95%(or 2.61%) per year.
(c)
using regression by MS-Excel, the cubic fir polynomial to this data set is
y = 0.4782x3 - 2850.7x2 + (6x106)x - (4x109)
where y-> number of enrollments, x-> year
(d)
(dy/dx) = 1.4346x2 - 5701.4x + (6x106)
put, x = 1990 in above expression for (dy/dx) to get rate of change at 1990
(e)
divide the value obtained in part(d) by 13819 and multiply by 100 to get answer
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