Question

use a calculator with a \\( y^x \\) key or a \\( \wedge \\) key to solve the following.\
the exponential function \\( f(x) = 551(1.032)^x \\) models the population of a country, \\( f(x) \\), in millions, \\( x \\) years after 1969. complete parts (a) - (e).\
\
\\( \boldsymbol{a.} \\) substitute 0 for \\( x \\) and, without using a calculator, find the country’s population in 1969.\
the country’s population in 1969 was \\( \square \\) million.

Explanation:

Step1: Identify the function and input

The function is \( f(x) = 551(1.032)^x \), and we need to find \( f(0) \) (since \( x = 0 \) corresponds to 1969).

Step2: Substitute \( x = 0 \) into the function

Using the exponent rule \( a^0 = 1 \) for any \( a
eq 0 \), we substitute \( x = 0 \) into \( f(x) \):
\( f(0) = 551(1.032)^0 = 551 \times 1 = 551 \).

Answer:

551