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.

See below

Step-by-step 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:

And the equation:

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

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.

when rotating a figure 180 degrees, imagine that you are able to take the figure and turn it clockwise or counterclockwise around a center point. to rotate a figure 180 degrees, you will need to apply the rule (x, y) → (-x, -y). start by using a coordinate grid with coordinates for each vertex of the figure. the center point of the coordinate grid is located at (0, 0), which is what you will rotate the figure around. write down the original coordinates of the shape you are going to rotate. then, apply the rule. for example, coordinate (1, 2) becomes (-1, -2). another example would be, coordinate (-4, -2) becoming (4, 2). after you change each original coordinate to the rotated coordinate, you will draw your new figure.

step-by-step explanation: