The table gives estimates of the world population, in millions, from 1750 to 200

Question

The table gives estimates of the world population, in millions, from 1750 to 2000. (Round your answers to the nearest million.)

200 6080

(b) Use the exponential model and the population figures for 1850 and 1900 to predict the world population in 1950.

__________ million people

(c) Use the exponential model and the population figures for 1900 and 1950 to predict the world population in 2000.
___________million people

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

200 6080

(b) Use the exponential model and the population figures for 1850 and 1900 to predict the world population in 1950.

__________ million people

(c) Use the exponential model and the population figures for 1900 and 1950 to predict the world population in 2000.
___________million people

Explanation / Answer

b) Population at yeat 1850 = 1260 million

Population at year 1900 = 1650 million

P(t) = Po*e^(rt)

1650 = 1260 * e^(50r)

1.30952 = e^(50r)

taking ln both sides we get

50r = ln(1.30952)

r = ln(1.30952)/50

Population at t=1950 will be 1260 * e^(ln(1.30952)/50 * 100) = 1260 * e^(2ln(1.30952)) = 2160.71 million

c) Population at yeat 1900 = 1650 million

Population at year 1950 = 2560 million

P(t) = Po*e^(rt)

2560 = 1650 * e^(50r)

1.551515 = e^(50r)

taking ln both sides we get

50r = ln(1.551515)

r = ln(1.551515)/50

Population at t=2000 will be 1650 * e^(ln(1.551515)/50 * 100) = 1650* e^(2ln(1.551515)) = 3971.87 million

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