To solve the problem and calculate the country's population based on the given exponential function, follow these steps:

Given Function:

$f(x) = 566 \cdot (1.032)^x$

where:

• $x = 0$ corresponds to the year 1973,
• $x = 22$ corresponds to the year 1995,
• $x = 44$ corresponds to the year 2017 (since 2017 - 1973 = 44).

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Step A: Population in 1973 ($x = 0$)

Substitute $x = 0$ into the function: $f(0) = 566 \cdot (1.032)^0$ Since any number raised to the power of 0 equals 1: $f(0) = 566 \cdot 1 = 566 \text{ million.}$

Thus, the population in 1973 is 566 million (as given).

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Step B: Population in 1995 ($x = 22$)

Substitute $x = 22$ into the function: $f(22) = 566 \cdot (1.032)^{22}$ Using a calculator:

1. Compute $(1.032)^{22}$:
   $(1.032)^{22} \approx 2.0003$
2. Multiply: $f(22) = 566 \cdot 2.0003 \approx 1132$

Thus, the population in 1995 is approximately 1132 million.

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Step C: Population in 2017 ($x = 44$)

Substitute $x = 44$ into the function: $f(44) = 566 \cdot (1.032)^{44}$ Using a calculator:

1. Compute $(1.032)^{44}$:
   $(1.032)^{44} \approx 3.5416$
2. Multiply: $f(44) = 566 \cdot 3.5416 \approx 2005.57$

Thus, the population in 2017 is approximately 2006 million (to the nearest million).

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Final Answers:

a. Population in 1973: 566 million
b. Population in 1995: 1132 million
c. Population in 2017: 2006 million

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Do you want further explanation or a breakdown of these steps?

Here are 5 questions to explore further:

1. How does an exponential growth model differ from linear growth?
2. Why does the base of the exponential function, $1.032$, indicate a growth rate of 3.2%?
3. What are some limitations of using exponential models for long-term population predictions?
4. How would the population change if the growth rate were higher or lower?
5. Can this model be adjusted for population decline instead of growth?

Tip: When solving exponential equations, always double-check your power calculations to ensure accuracy.