The population of a given country was 24.3 million on January 1,2001 and on January 1,2011 it was 27.3 million people and the population growth rate over this time period was g% compounded annually.At this same rate of growth g,how many more years (from January 1,2011)will it take this country's population to reach 30 million people?

Question

Quizplus · Accepted Answer

The correct answer is A because the population growth rate is g% compounded annually, so the population after t years is given by P(t) = 27.3 * (1 + g/100)^t. We want to find t such that P(t) = 30, so we solve the equation 27.3 * (1 + g/100)^t = 30. Taking the logarithm of both sides, we get t * log(1 + g/100) = log(30/27.3), so t = log(30/27.3) / log(1 + g/100). Plugging in the given values, we get t = log(30/27.3) / log(1 + 0.02) = 8.1 years.

The Population of a Given Country Was 24