Use a calculator with a $y^{x}$ key or a $\land$ key to solve the following.
The exponential function $f (x) = 540 (1.032)^{x}$ 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 country's population in 1968.
The country's population in 1968 was $◻$ million.

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Answer

$540$ million is the final answer.

Steps

Step 1 ：The exponential function $f (x) = 540 (1.032)^{x}$ models the population of a country, $f (x)$ , in millions, $x$ years after 1968.

Step 2 ：We are asked to find the country's population in 1968, which corresponds to $x = 0$ in the function.

Step 3 ：Substituting $x = 0$ into the function, we get $f (0) = 540 (1.032)^{0}$ .

Step 4 ：Since any number raised to the power of 0 is 1, the population in 1968 is $540 * 1 = 540$ million.

Step 5 ： $540$ million is the final answer.