SOLUTION: A.) Linear Growth A town has a fixed increase in population growth number of population increase each year. population 1897. Find the growth rates for the following I don't get

Question 92213: A.) Linear Growth A town has a fixed increase in population growth number of population increase each year. population 1897. Find the growth rates for the following
I don't get this at all?
Year (t) Population (P)
t = 0 Po = 1897
(2010)
t = 1
(2011)
t = 2
(2012)
t = 3
(2013)
t = 6
(2016)
B.) Find a linear equation in the form P = mt + b (y = mx + b), which gives the population, P, t years from 2010.
Answer by bucky(2189) (Show Source): You can put this solution on YOUR website!
If I understand your wording correctly, you are told that the initial population of the
town in 2010 is 1897. Each year that passes the town adds another 1897 persons.
.
So the population is projected to be:
.
In 2010 ... t=0 ... Population = 1897 <=== this is Po
In 2011 ... t=1 ... Population = 3794
In 2012 ... t=2 ... Population = 5691
In 2013 ... t=3 ... Population = 7588
In 2014 ... t=4 ... Population = 9485
In 2015 ... t=5 ... Population = 11382
In 2016 ... t=6 ... Population = 13279
and so on ...
.
The rate of change is 1897 per year. This will be the slope of the graph because each year
that passes results in an increase of 1897 in the population.
.
Using the equation form P=mt+b, we can replace m with 1897 to get:
.
P = 1897*t + b
.
in which t is the year of interest minus 2010.
.
Suppose our year of interest is 2010. Then t = 2010 - 2010 = 0
.
We know that in 2010 the population P is 1897. So we can substitute 1897 for P and 1897
for m to make the equation become:
.
1897 = 1897*0 + b
.
Do the multiplication on the right side to get:
.
1897 = 0 + b
.
This tells us that b is 1897. Substitute this value for b in the equation, and it becomes:
.
P = 1897t + 1897
.
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:
.
P = 1897*5 + 1897 = 9485 + 1897 = 11382
.
That is exactly as our table above said it would be.
.
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:
.
P = 1897*t + 1897
.
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:
.
P = 1897*20 + 1897
.
The multiplication on the right side makes the equation become:
.
P = 37940 + 1897 = 39837
.
In 2030 the population will be 39,837.
.
Hope this helps you to understand the problem a little better.
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