To find the country's population in 1969 using the function $f(x) = 569 \cdot (1.032)^x$, substitute $x = 0$:

$f(0) = 569 \cdot (1.032)^0$

Using the property of exponents, $(1.032)^0 = 1$, so:

$f(0) = 569 \cdot 1 = 569$

Thus, the country's population in 1969 was 569 million.

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Related Questions:

1. How does substituting $x = 1$ change the calculation?
2. What does the base $1.032$ represent in the context of population growth?
3. How can the formula be used to estimate the population in 10 years?
4. What happens to the population as $x \to \infty$?
5. How can logarithms help determine when the population will reach a certain value?

Tip:

When dealing with exponential functions, identifying the base helps you understand the growth rate directly.