Precalc question

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.

(a) When will Mexico double its 1987 population?

(b) When will the United States and Mexico have the same population?

Answer 1

Mexico: 82(1.025)^t

US: 244(1.007)^t

These are the populations of the two countries t years after 1987.

a) Mexico’s population will have doubled when it hits 164 = 2(82)

b) The two populations will be equal when these two expressions are equal to each other.

You’ll need a calculator that can do logs and to recall that the rule that log(x^y) = y log x.

Then, after you calculate the logs, you’ll have a simple linear algebraic equation in t to solve, in both cases. Hope that helps!

Note the question asks “When” not for t?