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The median household income in the US grew linearly from approximately $30, 000 in 1990 to $48, 000 in 2006. Let x be the number of years since 1990. Express the median income as a function of x. Use this function to approximate the median income in 2030. What is the significance of the slope of this function

Sagot :

MrRoyal

Answer:

[tex]y = 1125x+30000[/tex] --- The equation

The median income in 2030 is $75000

Step-by-step explanation:

Given

Represent years since 1990 with x and the income with y.

So, we have:

[tex](x_1,y_1) = (0,30000)[/tex] --- In 1990

[tex](x_2,y_2) = (16,48000)[/tex] --- In 2006

Solving (a): Express as a function.

First, we calculate the slope

[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]

[tex]m = \frac{48000-30000}{16-0}[/tex]

[tex]m = \frac{18000}{16}[/tex]

[tex]m = 1125[/tex]

The equation is then calculated as:

[tex]y = m(x-x_1)+y_1[/tex]

This gives:

[tex]y = 1125(x-0)+30000[/tex]

Open bracket

[tex]y = 1125x-0+30000[/tex]

[tex]y = 1125x+30000[/tex]

Solving (b): Income in 2030.

In 2030, x = 40.

Substitute 40 for x in [tex]y = 1125x+30000[/tex]

[tex]y = 1125*40 +30000[/tex]

[tex]y = 45000 +30000[/tex]

[tex]y = 75000[/tex]

Solving (c): The significance of the slope.

In (a), the slope is calculated as 1125.

This implies that the yearly rate is $1125

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