calc..exponential model for population growth?

Question

Year......Population
1750.....790
1800.....980
1850.....1260
1900.....1650
1950.....2560
2000.....6080

a) Use the exponential model and the population figures for 1750 and 1800 to predict the world population in 1900 and 1950. Compare with actual figures.

b) Use the exponential model and the population figures for 1850 and 1900 to predict the world population in 1950. Compare w/ actual figures.

c) Use the exponential model and the population figures for 1900 and 1950 to predict the world population in 2000. Compare with the actual population and try to explain the discrepancy.

Answer 1

a)
980/790 ≈ 1.2405
P = 790(1.2405)^((t - 1750)/10)
P(1900) = 790(1.2405)^((1900 - 1750)/50)
P(1900) ≈ 1,508
1,508/1,650 => - 8.6%
P(1950) = 790(1.2405)^((1950 - 1750)/50)
P(1950) ≈ 1,871
1,871/2,560 => - 26.9%

Basing projections on only 2 data points is rarely satisfactory.

Answer 2

World Population In 1900

Answer 3

World Population In 1800

Answer 4

a) From 1750 to 1800, 50 years passed and the population grew from 790 to 980 or 190 people

this equates to 190/50 people per year, or 3.8 people per year

To estimate growth from 1900 to 1950, we will add 50*3.8 to 1900's population:

1650 + 190 = 1840
This is much less than the actual (2560)

b) 1850 to 1900 = (1650 - 1260) / 50 = 7.8 people per year

1650 + (7.8 * 50) = 2040
This is also much less than the actual (2560) but is closer

c) 1900 to 1950 = (2560 - 1650) / 50 = 18.2 people per year

2560 + (18.2 * 50) = 3470
The is extremely less than the actual (6080)

The discrepancies occur because the 2nd power growth is not taken into account (that is, the later the year, the faster the growth per year).

Best of luck!

Answer 5

Why would anyone try to predict, with a non-linear model, using only 2 points? Makes no sense!
If you really want to use these data for predicting --Use MS-Excel to find the exponential model : y = 0.001e^(0.0076x)
Comparing this model results with actual:
Year--Actual--Predicted (with model)
1900--1650---1867
1950--2560---2731
2000--6080---3993

Answer 6

inhabitants develop is the replace in inhabitants via the years, and can be quantified because of the fact the replace interior the form of persons in a inhabitants consistent with unit time. The term inhabitants develop can technically consult with any species, yet very almost constantly refers to people, and that's regularly used informally for the extra specific demographic term inhabitants develop cost (see below), and is frequently used to refer extremely to the develop of the inhabitants of the worldwide. A logistic function or logistic curve fashions the S-curve of develop of a few set P. The preliminary degree of develop is approximately exponential; then, as saturation starts off, the develop slows, and at adulthood, develop stops.

Answer 7

Thanks for the answers everyone <3