Expert: Ahmed Salami - 10/2/2010

Question
If a population of A* PEOPLE GROWS AT A CONSTANT RATE OF R% PER YEAR,THE POPULATION AFTER T YEARS FORMS A GEOMETRIC PROGRESSION WITH A COMMON RATIO OR 1+R WRITE A FORMULA FOR THE TOTAL POPULATION IS INCREASING AT THE RATE 2% PER YEAR,HOW LONG WILL IT TAKE TO DOUBLE

Answer
Hi Janine,
The formula for the total population after t years is given by
P = A(1 + r)^t
For r = 2% = 0.02
P = A(1 + 0.02)^t
 = A(1.02)^t
When A is doubled, P = 2A, so
2A = A(1.02)^t
2 = (1.02)^t
Taking logarithm of both sides,
log 2 = log (1.02)^t
log 2 = t . log(1.02)
t = log 2 / log 1.02
= 0.3010/0.0086
= 35 years

Regards