An algebra problem by Dai Guico
Algebra
Level
3
The population, in thousands, of a country is where t is measured in years. How long will it take for the population to increase by 125 percent?
The answer is 40.
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1 solution
Let P(t) = x, and let after 'y' years the population will increase by 125% i.e. become 9x/4 , So, we get 10^8 * (1.5)^(t+y)/20 = 9/4 * 10^8 * (1.5)^t/20 . And we know, 1.5 = 15/10 = 3/2, so after aolving we are left with (3/2)^(y/20) = (3/2)^2. Therefore, y/20 = 2 , then y = 40