Use a calculator with a \(y^x\) key or a key to solve: India is currently one of the world’s fastest-growing countries. By 2040, the population of India will be larger than the population of China, by 2050, nearly one-third of the world’s population will live in these two countries alone. The exponential function \(f(x)=574(1.026)^x\) models the population of India, f(x), in millions, x years after 1974.
a. Substitute 0 for x and, without using a calculator, find India’s population in 1974.
b. Substitute 27 for x and use your calculator to find India’s population, to the nearest million, in the year 2001 as modeled by this function.
c. Find India’s population, to the nearest million, in the year 2028 as predicted by this function.