In 1990 the average family income was about $ 39 , 000 , and in 2010 it was about $ 70 , 768 . Let x = 0 represent 1990, x = 1 represent 1991, and so on. Find values for a and b so that f ( x ) = a x + b models the data A= _. B=__. What was the average family income in 2005?

Question

Dxaddy5837 Dxaddy5837

31-08-2020
Mathematics

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In 1990 the average family income was about $ 39 , 000 , and in 2010 it was about $ 70 , 768 . Let x = 0 represent 1990, x = 1 represent 1991, and so on. Find values for a and b so that f ( x ) = a x + b models the data A= _. B=__. What was the average family income in 2005?

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MrRoyal MrRoyal · Answer 1 · 2020-09-03T03:45:44+02:00

Answer:

[tex]f(x) = 1588.4x + 39000[/tex]

[tex]f(15) = 62826[/tex]

Step-by-step explanation:

Given

In 1990; Income= $39000

In 2010; Income= $70768

Solving (a): An equation in form of f(x) = ax + b

First, we need to determine the slope, a

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

Taking y as income and x as year index.

When x = 0; y = 39000

When x = 20; y = 70768

Substitute these values in the above formula

[tex]a = \frac{70768 - 39000}{20 - 0}[/tex]

[tex]a = \frac{31768}{20}[/tex]

[tex]a = 1588.4[/tex]

Next, is to determine the formula using:

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

Considering :When x = 0; y = 39000, we have

[tex]y - 39000 = 1588.4(x - 0)[/tex]

[tex]y - 39000 = 1588.4x[/tex]

Make y the subject of formula

[tex]y = 1588.4x + 39000[/tex]

Express y as a function of x

[tex]f(x) = 1588.4x + 39000[/tex]

Solving (b): Income in 2005

In 2005, x = 15

So:

[tex]f(x) = 1588.4x + 39000[/tex] becomes

[tex]f(15) = 1588.4 * 15 + 39000[/tex]

[tex]f(15) = 62826[/tex]

In 1990 the average family income was about $ 39 , 000 , and in 2010 it was about $ 70 , 768 . Let x = 0 represent 1990, x = 1 represent 1991, and so on. Find values for a and b so that f ( x ) = a x + b models the data A= _____. B=______. What was the average family income in 2005?

Respuesta :

Otras preguntas

In 1990 the average family income was about $ 39 , 000 , and in 2010 it was about $ 70 , 768 . Let x = 0 represent 1990, x = 1 represent 1991, and so on. Find values for a and b so that f ( x ) = a x + b models the data A= _. B=__. What was the average family income in 2005?