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.

\(\displaystyle{F}{\left({x}\right)}={574}{\left({1.026}\right)}^{{x}}\)

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.