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?

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

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

Next, is to determine the formula using:

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

Make y the subject of formula

Express y as a function of x

Solving (b): Income in 2005

In 2005, x = 15

So:

becomes

problem:

f(x) = - 2/3x + 5; f(5/2)

substitute 5/2 in for x:

f(5/2) = -2/3(5/2) + 5

simplify the right side:

f(5/2) = -5/3 + 5

f(5/2) = 10/3

f(5/2) = 10/3

i hope this !