Question

The graph shows the projections in total enrollment at degree granting institutions from Fall 2003 to Fall2012The linear model, y= .2145x + 15.79, provides the approximate enrollment, in millions, between the years 2003 and 2012,to 2004, and so on, and y is in millions of students(a) Use the model to determine projected enrollment for Fall 2008.The projected enrollment for Fall 2008 is 16.9 millions. This is answered. (Type an integer or decimal rounded to the nearest tenth as needed.)(b) Use the model to determine the year in which enrollment is projected to reach 17 million.(Round down to the nearest year)2008. This is answered(c) they are quite close. This is answered. This is the one i need help with part D.(d) The enrollment in Fall 1993 was 14.3 million. The model here is based on data from 2003 to 2012. If you were to use the model for 1993, what would the enrollment be?

Answer 1

We are given the relation

`y=0.2145x+15.79`

Answer 2

The estimated enrollment and year are:

a) 16.9 million

b) year 2009

c) quite close

d) 13.6 million

How the estimated enrollment were calculated

a) Given

y = 0.2145x + 15.79

model for 2003

In 2003 x = 0

In 2008, x = 5

y(5) = 0.2145(5) + 15.79

= 1.0725 +15.79

= 16.88 = 16.9 million

b)

y = 0.2145x + 15.79

When the is 17 million

17 = 0.2145x + 15.7

0.2145x = 17-15.79

0.2145x = 1.21

x = 1.21/0.2145

x = 5.6 approx 6

Therefore,

20083 +6 = 2009

By 2009 there will be 17 million.

c) They are close

(d) The enrollment in 1993 was 14.3 million. The model here is based on data from 2003 to 2012.

Given

y = 0.2145x + 15.79

This represents the model for 2003, to estimate the enrollment in 1993

Count from 2003 to 1993 which is 10 years but in the negative direction.

Therefore, x = -10

y(-10) = 0.2145(-10) + 15.79

= -2.145 + 15.79

= 13.6 million