Germany population keynote
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This document summarizes different methods for predicting the future population of Germany in 2061 using historical population data from 1850, 1950, and 2000. A linear prediction model estimates the population will be around 100 million. A quadratic prediction model estimates around 118 million. An exponential/logarithmic prediction model estimates around 105 million.
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- 1. Germany Population By Evan Franz
- 3. Making a prediction with a line. This is done by taking two points and drawing a line through them. We take the corresponding years and population and put them into the linear equation.
- 4. It will look somewhat like this. 1850 is referred to as year 0 because it is the year we started with. The points i used for this are year 100(1950) and year 150(2000). These are used as the X values with the populations as the Y values.
- 5. y1-y2 = Slope y-y1=m(x-x1) x1-x2 68377000-82797400 =288408=Slope 100-150 y-68377000=288408(x-100) y-68377000=288408x-28840800 +68377000 +68377000 y=288408x+39536200 We then plug in the year that we want to predict the population. 2061=211 y=288408(211)+39536200 y=100390288 Predicted population of Germany in 2061~100,390,288
- 6. Making a prediction with a Quadratic We need to chose 3 points for this prediction. we will plug these points into the equation ax^2+bx+c and use them to find the values of a b and c. We also need to write the populations in a much more manageable way. We write them in scientific notation, moving the decimal over 7 places.
- 8. x1,y1 0,3.5 3.5=a(0)^2+b(0)+c 3.5=a(0)^2+b(0)+c x2,y2 100,6.8 6.8=a(100)^2+b(100)+c 3.5=0+0+c x3,y3 110,7.2 7.2=a(110)^2+b(110)+c 3.5=c 6.8=a(100)^2+b(100)+3.5 7.2=a(110)^2+b(110)+3.5 3.7=12100a+110(.033-100a) 3.3=10000a+100b 3.7=12100a+3.63-11000a 100 3.3=10000a+100b .07=1100a 3.7=12100a+110b .033-100a=b 1100 3.3=10000(.00006)+100b a=.00006 b=.027 3.3=.6+100b 2.7=100b Our Equation. y=.00006x^2+.027x+3.5 100 Now we plug in the year we want to predict (211) once again as the x value. y=.00006(211)^2+.027(211)+3.5 Predicted population: y=.2.67126+5.697+3.5 118,682,600
- 10. 68=ab^100 y=ab^x y=population, x=years 83=ab^150 a=68/b^100 a=83/b^150 68=a(1.00399)^100 68=a1.48984 68 83 1.48984 1.48984 b^100 = b^150 a=45.64249 68b^150=83b^100 b^100 b^100 Now we use these 2 points 68b^50=83 in the origanal equation 68 68 y=(45.64249)(1.00399)^211 b^50=1.22059 b=1.00399 y=(45.64249)(2.31686) y=105.74748 Predicted Population: 105,747,480
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