Questions: The per capita (per person) income from 1980 to 2010 can be modeled by f(x)=1000(x-1980)+15,000 where x is the year. Determine the year when the per capita income was 24,000. The per capita income was 24,000 in the year

Solution Steps

To determine the year when the per capita income was 24,000, we need to solve the equation \( f(x) = 24,000 \) for \( x \). Given the function \( f(x) = 1000(x - 1980) + 15,000 \), we can set it equal to 24,000 and solve for $x$.

We are given the function for per capita income: $$f(x) = 1000(x - 1980) + 15,000$$ We need to determine the year $x$ when the per capita income was \$24,000. Therefore, we set up the equation: \[ 1000(x - 1980) + 15,000 = 24,000 \]

First, subtract 15,000 from both sides of the equation: $$1000(x - 1980) = 24,000 - 15,000$$ $$1000(x - 1980) = 9,000$$

Next, divide both sides by 1000: $$x - 1980 = \frac{9,000}{1000}$$ $$x - 1980 = 9$$

Finally, add 1980 to both sides to solve for $x$: $$x = 9 + 1980$$ $$x = 1989$$

Final Answer