 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. bobbie71G 2021-09-22 Answered
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 $$\displaystyle{f{{\left({x}\right)}}}={574}{\left({1.026}\right)}^{{x}}$$ models the population of India, f(x), in millions, x years after 1974. Find India’s population, to the nearest million, in the year 2055 as predicted by this function.

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The following exponential function
$$\displaystyle{F}{\left({x}\right)}={574}{\left({1.026}\right)}^{{x}}$$
models the population of India after 1974. Thus
To find the population of India in the year 2055 from this function, we find the value of x which represent number of years after 1974, then Number of years in the year 2055 and after 1974 is
x= 2055 —1974= 81
Then, the population of India in the year 2055 from the function given in equation (1) is
$$\displaystyle{f{{\left({81}\right)}}}={574}{\left({1.026}\right)}^{{81}}$$
Calculating the approximate value of the population of India in the year 2055 using a scientific and graphing calculator, respectively as follows
Scientific calculator: $$\displaystyle{574}\cdot{\left({1}.{.26}\right)}{y}^{{x}}{81}=$$ and
Graphing calculator: $$\displaystyle{574}\cdot{\left({1.026}\right)}^{{81}}$$ ENTER
This should approximately by $$\displaystyle{f{{\left({81}\right)}}}={574}{\left({1.026}\right)}^{{81}}\sim{4590.37}$$ millions
Then, the population of India in the year 2055 will te 4590.37 millions.