Question

In 1987, the population of Mexico was estimated at 82 million people, with an annual growth rate of 2.5%. The 1987 population of the United States was estimated at 244 million with an annual growth rate of 0.7%. Assume that both populations are growing exponentially. When will Mexico double its population?

Answer 1

P_Mexico = 82(1.025)^t where t is the number of years past 1987

164 = 82(1.025)^t
2 = 1.025^t
take log of both sides
log 2 = log 1.025^t
log 2 = t(log 1.025)
t = log 2/log 1.025
= 28.07

so add 28 to 1987