Question

The exponential function f(x) models the population of a country, f(x), in millions, x years after . Complete parts (a)(e).a. Substitute 0 for x and, without using a calculator, find the country's population in The country's population in was nothing million.

Answer 1

Given:

The exponential model is,

$f(x)=557(1.026)^x$

The function f(x) denotes the population of a country in millions x years after 1968.

a) Put x = 0,

$\begin{gathered} f(x)=557(1.026)^x \\ f(x)=557(1.026)^0 \\ =557(1) \\ =557 \end{gathered}$

Answer: Country's population in 1968 was 557 million

b) In the year 1995 the country's population will be,

$\begin{gathered} \text{ In the 1995 year means after 27 years from 1968} \\ \text{For x=27} \\ f(x)=557(1.026)^x \\ =557(1.026)^{27} \\ =557\times\: 1.99976 \\ =1113.868535 \end{gathered}$

Answer: In the year 1995 the population is 1113.868535 million.