A piece of property was purchased for $25,000 in 1970. Each year the value has increased at a rate of $1,500 per year. In 2000 the property is worth $70,000. A plot of value versus time shows that the points lie on a straight line.
The owner decided when the property was purchased that she would sell it when its value reached $100,000. IF the rate of increase remains constant then you could estimate when the this will occur by simply extrapolating the linear relationship and finding out where the line intersects the value of $100,000 on the Y-axis.
Note that in this relationship the two variables (time and value) increase together. As time has increased the value has gone up. Such relationships are said to be positive and the line fitting the points has a positive slope. If the property value were to decrease as time increased the relationship would be said to be negative and the fitted line would have a negative slope.
Carefully place the edge of a piece of paper on the screen so that the edge goes through as many o the points as possible.
Estimate the discharge when the stage is 11 feet.
Knowing the rate of change (the slope of the line) you can calculate exactly when the value will be $100,000 if you assume that extrapolation makes sense. The calculated year in which the value will reach $100,000 is:
In this case extrapolation was "easy" as the relationship was linear and we know that all of the points (such as the value each year) will lie on the same straight line.
You will encounter many situations in which an extrapolation is used in making a prediction. Always ask your self if it is reasonable to extrapolate. Perhaps the economy will change and prices decline in 2001. Or perhaps the property will increase in value at a greater rate. Check to see what justification the author gives for assuming it is appropriate to extrapolate the known relationship.
Return