Problem
Use a calculator with a $y^{\mathrm{x}}$ key or a $\wedge$ 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 $\square$ million.
Solution
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 ：\(\boxed{540}\) million is the final answer.
