The CIA estimates the world population is growing at a rate of 1.167?% each year. The world population for 2007 was about 6.6 billion. Write an equation for the world population after n years.
Let P be the population at any time t.
According to the given problem
dP/dt = (1.167/100)P
dP/P = (1.167/100) dt
Integrating both sides
logP = (1.167/100)t + C1
P =Ce^[(1.167/100)t]
After n years Put t=n
P = Ce^[(1.167/100)n]
Where C is a constant value.
for n = 2007, the value of P = 6.6 billion
6.6 = Ce^[(1.167/100)2007]
6.6 = C e^23.42
C = 6.6/e^23.42 = 14831216154
Therefore
P = 14831216154 e^[(1.167/100)n]