A village was founded four hundred years ago by a group of 20 people. In this village, the population triples every one hundred years. What is the population of the village today?

Answer:Step-by-step explanation:Treat this like compound interest:  Use A = P(1 + r)^t.Here, P is the initial population and A is 3 times that, or 3P.  Since P = 20 people, 3P = 60 people,and this population is reached after 100 years.We need to determine r, substitute its value into the formula A = P(1 + r)^t, and then determine the population of the village after 400 years.60 = 20(1 + r)^100Simplifying, 3 = (1 + r)^100.Taking the natural log of both sides,ln 3 = 100 ln (1 + r), or                    ln 3ln (1 + r) = ---------------                     100               = 1.0986 / 100 = 0.01986We must solve this for r.  Raising e to the power ln (1 + r), on the left side of an equation, and raising e to the power 0. 01986 on the right side, we get:1 + r = 3, so r must = 2.Now find the pop of the village today.  Use the same equation:  A = P (1+r)^t.A = 20(1 +2)^4 (hundreds), or A = 20(3)^4, orA = 81The population after 400 years is 81.