The current world population is about 7 billion. Under current conditions the population is growing exponentially with a yearly growth factor of 1.014. In parts (b) and (c), round your answers to the nearest year.
(a) Find a formula that gives the world population N, in billions, after t years.
(b) How long will it take the population to double?
(c) How long after doubling will it take for the population to double again?
+130536 (a)
N = N0 (1.014)t where N0 is the initial population, t is in years and N is the population after t years
(b)
2N0 =N0 (1.014)t divide through by N0
2 = (1.014)t take the log of both sides
log 2 = log (1.014)t and by a log property we can write
log 2 = t * log (1.014) divide both sides by log(1.014)
log 2 / log 1.014 = t = about 49.85 yrs = 50 yrs
(c) If it doubles again, it is 4 times the original number, i.e., 4N0....and we can solve this :
log 4 / log 1.014 = t = about 99.71 yrs = 100 yrs
So......it takes about 50 years to double again
Part (c) was edited for an original mistake......!!!!!!
