Question

algebra
name: taye banks jr
date:
scatter plot assignment
10 points
pick a country (cannot be the same as other group members):

1. now use the internet to find the population for 8 different years after the year 2000. the years do not need to be consecutive. write your findings in the table.
2. scale the graph below, plot your data, and draw a line of best fit.

years after 2000	population (in ______)

1. write the equation for your line of best fit (show work below): $y = $ ____ $x + $ ____
2. use your function to predict the population in the year 2050:

Explanation:

Step 1: Choose a Country

Let's pick the United States. Now, we'll find the population for 8 different years after 2000. We can use reliable sources like the World Bank or the US Census Bureau.

• Year 2000: \( x = 0 \), Population (in millions) \( y = 282.2 \)
• Year 2005: \( x = 5 \), Population \( y = 295.5 \)
• Year 2010: \( x = 10 \), Population \( y = 308.7 \)
• Year 2015: \( x = 15 \), Population \( y = 321.4 \)
• Year 2020: \( x = 20 \), Population \( y = 331.9 \)
• Year 2025: \( x = 25 \), Population (projected) \( y = 342.6 \)
• Year 2030: \( x = 30 \), Population (projected) \( y = 353.5 \)
• Year 2035: \( x = 35 \), Population (projected) \( y = 364.6 \)

Step 2: Plot the Data and Draw Line of Best Fit

We'll scale the x - axis as "Years After 2000" and the y - axis as "Population (in millions)". Plot the points \((0, 282.2)\), \((5, 295.5)\), \((10, 308.7)\), \((15, 321.4)\), \((20, 331.9)\), \((25, 342.6)\), \((30, 353.5)\), \((35, 364.6)\). Then, draw a line that best fits these points. Looking at the trend, the line seems to have a positive slope.

Step 3: Find the Equation of the Line of Best Fit

The general form of a linear equation is \( y=mx + b \), where \( m \) is the slope and \( b \) is the y - intercept.

• First, calculate the slope \( m \). We can use two points, say \((0, 282.2)\) and \((35, 364.6)\).

The slope formula is \( m=\frac{y_2 - y_1}{x_2 - x_1} \)
\( m=\frac{364.6 - 282.2}{35 - 0}=\frac{82.4}{35}\approx2.354 \)

• The y - intercept \( b \) is the value of \( y \) when \( x = 0 \). From the point \((0, 282.2)\), we see that \( b = 282.2 \)

So the equation of the line of best fit is \( y = 2.354x+282.2 \)

Step 4: Predict the Population in 2050

For the year 2050, the number of years after 2000 is \( x=2050 - 2000 = 50 \)
Substitute \( x = 50 \) into the equation \( y=2.354x + 282.2 \)
\( y=2.354\times50+282.2 \)
\( y = 117.7+282.2=399.9\) (in millions)

Answer:

1. Table (using United States):

Years After 2000	Population (in millions)
5	295.5
10	308.7
15	321.4
20	331.9
25	342.6
30	353.5
35	364.6

1. (Graph plotting: Points plotted as above and line of best fit drawn)

1. Equation of line of best fit: \( y = 2.354x+282.2 \)

1. Predicted population in 2050: \( 399.9 \) million (or approximately 400 million)