Blake Nielsen, Peter Jorgensen
Math 1010
Utah Population
30
25
20
15
Population (100,00)
10
5
0
1.
0
5
10
15
20
25
30
2. Coordinates of two points, we looked at the graph and the data respectively
and chose two points from the data. These two points are (5,16), (25,25)
3. 25-16 = 9
25-5 20
The formula used above is the formula used to find slope, which is
Y2-Y1
X2-X1.
Then we will use the following formula, the point slope formula to form a
linear function.
f(x)=(y-y1)=m(x-x1)
First, we will select one coordinate from a point on the graph, X1 and Y1 we
will use (5,16).
Second, we will take this point as well as the slope we found earlier
(m=slope) and plug it into the equation, giving us,
f(x)= (y-16)=9/20(x-5).
4. Now we will show the slope of the line.
m=9/20.
What this tells us is that on a graph, when one point is found, the next point
will be up 9 units and to the right 20 units. Yes, however the slope does
change in between other points on this graph.
Blake Nielsen, Peter Jorgensen
Math 1010
5. Now we will find the value of f(45) using the function we made for part 3.
f(45)=(y-16)=9/20(x-5)
Now I will substitute “45” for “x”.
f(45)= (y-16)=9/20(45-5)
Now I will distribute the slope to the (45-5).
f(45)= (y-16)=(405/20-45/20)
I will now simplify by subtracting the fractions.
f(45)= (y-16)=(360/20)
I will now simplify further by dividing 360 and 20 by 10, because they are both
divisible by 10, this will simplify the fraction a bit.
f(45)= (y-16)=(36/2)
Now I will multiply the entire equation by 2 to remove the fraction.
f(45)= 2(y-16)=2(36/2)
I will now distribute the 2 into the parenthesis to simplify.
f(45)= 2y-32=36
Now I will isolate the variable “y” by adding 32 on each side.
f(45)= 2y=68
Now I can divide by 2 on each side to find the value of y.
f(45)=y=68/2
I can take away the first equal sign and the y variable because f(45) is the y
magnitude at x=45.
f(45)=68/2=34
This means that according to this function, the population of Utah will equal
3,400,000 (3.4 million) 45 years after 1980, which is 2025.
Blake Nielsen, Peter Jorgensen
Math 1010
6. Now I will approximate what year the residential population of Utah reached
2,000,000.
First, I will take the linear function from step 3 and plug in 20 for f(x) which
is equal to Y. (representing 2,000,000)
When converted, the equation will look as follows,
Y=(9/20)x+(55/4)
20=(9/20)x+(55/4)
Now I will subtract (55/4) from 20
20- (55/4)=(9/20)x
This gives me the new equation of
6.25=(9/20)x
Next, I will divide 6.25 by (9/20) giving us,
6.25/(9/20)=x
This gives us the solution,
13.89=x
So, in order to reach 2,000,000 from the year 1980, we take our solution and add it
into 1980, this gives us the conclusion that Utah’s population reached 2,000,000 in
the year 1994.
7. Now we’ve found a function to compare to.
The function oddly enough is the same as the one we used
f(x)=(y-16)=9/20(x-5)
I believe these functions are the same because the numbers on the line are
fairly simple to point out, using the larger point on the graph, (25,25) is
simple and will not give you an improper fraction as a slope, and they can
eventually be broken down into small enough components to work with.
Also, due to the fact that it is a straight line graph we are working with, there
are only so many options for people to choose, and this being one of the
Blake Nielsen, Peter Jorgensen
Math 1010
more convenient one to choose, it is understandable as to why more than one
group chose to do it.
8. Using a linear equation to estimate growth such as this has several
drawbacks, the most prevalent of which is that it is imprecise and only gives
a rough estimate of the growth, whereas using exact points and components
will respectively, give more exact answers and estimations.