Question

The population of Champaign, Illinois is given for three years in the table below:

Year Population
1970 163488
1980 168392
2012 203276

(a)Using 1970 as t=0, create a linear model
from the first two data points in this table to
predict the population, p, as a function of the
number of years since 1970, t.

(b) If this model is used to predict the population of Champaign in the year 2012, will the model over estimate or underestimate the actual population? Explain.

Answer 1

See below

Explanation:

a) Using the first two lines to get the equation:

Since t = 0 represents a start point, the y-intercept is 163488

Slope is:

• (168392 - 163488)/10 = 490.4

And the equation:

• P(t) = 490.4(t - 1970) + 163488

b) Prediction of the population in 2012 using the function:

• P(2012) = 490.4(2012 - 1970) + 163488 = 184084.8

As we see the number we got is less than the one on the line 3 of the table. So the model underestimated the actual population.