4. Exponential Population Growth & Doubling Time. The population of the world in

Question

4. Exponential Population Growth & Doubling Time. The population of the world in 1800 was 0.9 billion. a. What exponential rate of growth would have resulted in the population in 1960, which was 3 billion? (Answer:r-7.5*103 yr') At this growth rate, what is the doubling time for this population? (Answer: Td 92.4 yrs) If this rate continued, what would the population have been in the year 2015? (Answer: N 4.5 1094.5 billion) Is your answer for part c) larger or smaller than the actual world population in 2015? What does this result mean in terms of how the rate of growth changed between 1800-1960 and 1960-2015? b. c. d.

Explanation / Answer

a)

here growth model F= A*ert where F =future value=3 billion; A =present value=0.9 billion

r=rate and t=number of years =1960-1800=160

hence 3=0.9*er*160

er*160 =3.333

taking log and solving

r*160 =ln(3.333)

r=ln(3.333)/160 =0.0075 =7.5*10-3 /years

b)

here final population =2A

hence 2A=A*e0.0075t

e0.0075t =2

taking log on both sides

t=ln(2)/0.0075 =92.4 years

c)

for A =3 ; r =0.0075 and t =2015-1960=55

hence popualtion in 2015 F =3*e0.0075*55 =4.53 billion

d)

this is smaller than actual world population in 2015

this means that rate of population growth has increased from 1960-2015 than it was from 1800-1960

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