Chapter 14.4, Problem 25E

(a)

To determine

To Find: The equation to model the enrolment as the function of the number of years since 1965.

Answer to Problem 25E

The required model is $y=-0.04567x^3-271.5x^2+537844.86x-355179573$ .

Explanation of Solution

Given:

The given data is shown in Table 1

Table 1

Year	1965	1970	1975	1980	1990	1995	2000
Enrolment	365	458	468	468	426	556	629

Calculation:

Consider the scatter plot for the given data is shown in Figure 1

  

Figure 1

Observe the above figure the model shows that data is cubic polynomial and it has one minimum and maximum.

By the use of graphing calculator the sample model represents the above data as shown in Figure 2

  

Figure 2

Thus, the required sample model is $y=-0.04567x^3-271.5x^2+537844.86x-355179573$ .

(b)

To determine

To Find: The prediction for the enrolment in 2015.

Answer to Problem 25E

The prediction for the enrolment is $-747415676.6$ .

Explanation of Solution

Consider the model is $y=-0.04567x^3-271.5x^2+537844.86x-355179573$ .

Then,

  $\begin{array}{c}y=-0.04567{\left(2015\right)}^3-271.5{\left(2015\right)}^2+537844.86\left(2015\right)-355179573\\ =-747415676.6\end{array}$