Consider the population model: $P(x)=\frac{1,690+400 x}{10+0.01 x}$, where $x$ is time in years. During which year will the population reach 1,000 ? Enter a whole number. Note: the value 6.23 would actually correspond to the 7 th year.

Step 1 ：Consider the population model: \(P(x)=\frac{1,690+400 x}{10+0.01 x}\), where \(x\) is time in years.

Step 2 ：We need to find the year when the population will reach 1000. This means we need to solve the equation \(P(x) = 1000\) for \(x\).

Step 3 ：Since the population model is a rational function, we can solve this equation by cross-multiplication and then solving the resulting quadratic equation.

Step 4 ：The solution to the equation is approximately 21.31.

Step 5 ：However, the question asks for the year when the population will reach 1000, and it specifies that we should round up to the nearest whole number. Therefore, we should round 21.31 up to 22.

Step 6 ：Final Answer: \(\boxed{22}\)