Question

the median family income in country x between 1990 and 1999 can be modeled by the function i(x) = 1,149.5(x - 1990) + 35,914, where x is the year. determine symbolically when the median income was $42,618. \
\
a. $x \approx 1994$ \
b. $x \approx 1998$ \
c. $x \approx 1996$

Explanation:

Step1: Set up the equation

We know that \( I(x) = 1149.5(x - 1990)+35914 \) and we want to find \( x \) when \( I(x)=42618 \). So we set up the equation:
\( 1149.5(x - 1990)+35914 = 42618 \)

Step2: Subtract 35914 from both sides

Subtract 35914 from each side of the equation to isolate the term with \( x \):
\( 1149.5(x - 1990)=42618 - 35914 \)
Calculate the right - hand side: \( 42618-35914 = 6704 \)
So we have \( 1149.5(x - 1990)=6704 \)

Step3: Divide both sides by 1149.5

Divide both sides of the equation by 1149.5:
\( x - 1990=\frac{6704}{1149.5} \)
Calculate \( \frac{6704}{1149.5}\approx5.83 \) (we can do this division: \( 6704\div1149.5\approx5.83 \))

Step4: Solve for x

Add 1990 to both sides of the equation:
\( x=1990 + 5.83\approx1995.83\approx1996 \)

Answer:

C. \( x\approx1996 \)