The population of a town in three consecutive years are 5000, 7000 and 8400 respectively. The population of the town in the fourth consecutive year according to geometrical increase method is

POPULATION IN FIRST' YEAR P1= 5000
POPULATION IN SECOND YEAR P2= 7000
INCREMENT. I= 7000-5000=2000
GEOMETRICAL RATE GROWTH G1= 2000/5000= 0.4
POPULATION OF THIRD YEAR P3= 8400
INCREMENT I =8400-7000=1400
GEOMETRICAL RATE GROWTH G2=1400/7000=0.2
AVERAGE GEOMETRICAL MEAN[GM]
= G1+G2/2
= 0.4+02/2
= 0.3
POPULATION OF FOURTH YEAR P4 = P3[1+GM]
=8400[1+0.3]
= 10920
IN FOURTH CONSECUTIVE YEAR THE PROJECTED POPULATION IS 10920
OPTION D IS CORRECT ANSWER

Pn=P(1+IG/100)n

IG - Percentage growth rate which is 30%

Pn= 8400+30/100*8400=10920

Grow Rate- r1=2000÷5000×100=40
r2=1400÷7000×100=20
Now geometrical grow rate
r%=√(40+20=28.284
geometrical increases
P=p(1+r)^n
P=8400[1+(28.284÷100)^1]
P=10775.5 ans