Question

use a calculator with a \\( y^x \\) key or a \\( \wedge \\) key to solve the following. the exponential function \\( f(x) = 574(1.032)^x \\) models the population of a country, \\( f(x) \\), in millions, \\( x \\) years after 1968. complete parts (a) - (e). a. substitute 0 for \\( x \\) and, without using a calculator, find the countrys population in 1968. the countrys population in 1968 was \\( \square \\) million.

Explanation:

Step1: Substitute x=0 into the function

We have the function \( f(x) = 574(1.032)^x \). Substitute \( x = 0 \) into it: \( f(0)=574(1.032)^0 \).

Step2: Simplify the exponential term

Recall that any non - zero number to the power of 0 is 1, so \( (1.032)^0 = 1 \). Then \( f(0)=574\times1 \).

Step3: Calculate the result

\( 574\times1 = 574 \).

Answer:

574