QuestionThe population of a small town in central Florida has shown a linear decline in the years 1989-2001. In 1989 the population was 35900 people. In 2001 it was 26900 people. A) Write a linear equation expressing the population of the town, , as a function of , the number of years since 1989. Answer: B) If the town is still experiencing a linear decline, what will the population be in 2006?
Studdy Solution
STEP 1
1. The population decline is linear from 1989 to 2001.
2. In 1989, the population was 35,900 people.
3. In 2001, the population was 26,900 people.
4. We need to express the population as a function of time since 1989.
5. We need to predict the population in 2006 assuming the decline continues linearly.
STEP 2
1. Determine the slope of the linear decline.
2. Write the linear equation for the population as a function of time.
3. Use the equation to predict the population in 2006.
STEP 3
Determine the slope of the linear decline.
The slope of the line is given by the change in population divided by the change in time. The change in population from 1989 to 2001 is:
The change in time from 1989 to 2001 is:
Thus, the slope is:
STEP 4
Write the linear equation for the population as a function of time.
The linear equation is in the form , where is the population at (the year 1989).
Since , the equation becomes:
STEP 5
Use the equation to predict the population in 2006.
First, determine for the year 2006:
Substitute into the equation:
Calculate:
The population in 2006 is:
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