SOLUTION: Q: A town with the initial population, Po, in the year 2010. The initial population is 1000. I must use this value of Po. The town has a fixed increase in population growth num

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Question 92104: Q: A town with the initial population, Po, in the year 2010. The initial population is 1000. I must use this value of Po. The town has a fixed increase in population growth number each year. This is 1000. I must fill in the following chart:
__________________________
Year (t) Population
t=0 Po=
(2010)
__________________________
t=1
(2011)
__________________________
t=2
(2012
__________________________
and so on until (2016)
then I must find a linear equation in the form P=mt+b(y=Mx+b, which gives the population, P, t years from 2010. How would I explain it and break it down?
Answer by bucky(2189) (Show Source):
You can put this solution on YOUR website!
You are told that the initial population of the town in 2010 is 1000. Each year that passes
the town adds another 1000 persons.
.
So the population is projected to be:
.
In 2010 ... t=o ... Population = 1000 <=== this is Po
In 2011 ... t=1 ... Population = 2000
In 2012 ... t=2 ... Population = 3000
In 2013 ... t=3 ... Population = 4000
In 2014 ... t=4 ... Population = 5000
In 2015 ... t=5 ... Population = 6000
and so on ...
.
The rate of change is 1000 per year. This will be the slope of the graph because each year
that passes results in an increase of 1000 in the population.
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Using the equation form P=mt+b, we can replace m with 1000 to get:
.

.
in which t is the year of interest minus 2010.
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Suppose our year of interest is 2010. Then t = 2010 - 2010 = 0
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We know that in 2010 the population P is 1000. So we can substitute 1000 for P and 1000
for m to make the equation become:
.

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Do the multiplication on the right side to get:
.

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This tells us that b is 1000. Substitute this value for b in the equation, and it becomes:
.

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Let's check this out. Suppose the year we are interested in finding the population
is 2015 ... 5 years after 2010 so that t = 5. Substitute t = 5 and the equation becomes:
.

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That is exactly as our table above said it would be.
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So all you have to do is pick a year for wish you want to find the population. Subtract
2010 from that year. Use the result of that subtraction as the value of t in the equation:
.

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For example. Suppose the year you are interested in finding the population for is 2030.
Subtract 2010 from 2030 and get 20 for the value of t. Substituting 20 for t results in
the equation becoming:
.

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The multiplication on the right side makes the equation become:
.

.
In 2030 the population will be 21,000.
.
Hope this helps you to understand the problem a little better.