Question 123628
If I understand your problem correctly you are to find an equation in the form:
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{{{P = mT + B}}}
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That will enable you to determine what the population will be some time in the future.
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As you have recognized, this equation is in the slope-intercept form in which m is the slope
of the graph and B is the point where the graph intercepts the y-axis.
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The letters above will represent the following quantities: P = population, m (the slope of
the graph) will represent the rate of change in the population, T will represent the number
of years that go by, and B is the known population at some point in time when T = 0.
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You are told that the increase in population is 100 per year. That means that m equals 100.
Think of it this way ... how much will the population increase if 2 years go by? The answer
is 100 times 2 ... which is 100 times T. In 3 years the population would increase 
by 100 times 3. It increases by m times T or 100*T and since T = 3 years, it goes up
by 100*3 or 300.
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So now we can write the equation as:
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{{{P = 100T + B}}}
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The problem then tells you that the base year is 2010. That is when T equals 0. If I interpret
your numbers correctly, in the year 2010 (when T = 0) the population will be 2500. If you
look at our equation and set T = 0, you get that P, the population, equals B. Since the
population is known to be 2500 at that time, the B must be 2500. Substituting this value
for B results in the equation becoming:
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{{{P = 100T + 2500}}}
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That should be the equation you are looking for. Just recognize that T is equal to the number
of years beyond 2010.
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Using this equation you could now calculate the population in any year from 2010 on. For example,
in the year 2016 (which is 6 years after 2010 meaning that T = 6) the population would be 
expected at:
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{{{P = 100*T + 2500 = 100*6 + 2500 = 600 + 2500 = 3100}}}
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So the population in 2016 could be expected to be 3100 persons.
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Hopefully this answers your questions and if it doesn't at least it might give you enough insight
to see your way through to an answer.