The table gives the population of India, in millions, for the second half of the

ID: 3343113 • Letter: T

Question

The table gives the population of India, in millions, for the

second half of the 20th century.

Year Population

1951 361

1961 439

1971 548

1981 683

1991 846

2001 1029

(a) Use the exponential model and the census figures for 1951

and 1961 to predict the population in 2001. Compare with

the actual figure.

(b) Use the exponential model and the census figures for 1961

and 1981 to predict the population in 2001. Compare with

the actual population. Then use this model to predict the

population in the years 2010 and 2020.

; (c) Graph both of the exponential functions in parts (a) and

(b) together with a plot of the actual population. Are these

models reasonable ones?

dP/dt =kP

P = Ae^(kt)

361=Ae^(1951k)

439=Ae^(1961k)

439/361 = e^(10k)

10k=ln(439/361)

P(2001) = Ae^(2001k) = 361e^(50k) = 361*(439/361)^5 = 960.05

(b)683=Ae^(1981k)

683/439 = e^(20k)

20k = ln(683/439)

k=0.05ln(683/439)

A=683/e^(1981k)

P(2001) = Ae^(2001k) = 683e^(20k) = 1062.61

P(2010) = 683e^(29k) = 683(683/439)^(29/20)=1296.45

P(2020) = 683e^(39k) = 683(683/439)^(39/20)=1617.1

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