Question

In 1992 the average family income was about 42000, and in 2002 it was about 56256. Let x = 0 represent 1992, x = 1 represent 1993, and so on. Find values for a and b (rounded to one decimal place if necessary) so that f ( x ) = a x + b models the data a = b = What was the average family income in 1997? $

Answer 1

Explanation:

Given the function that models the income of a family as g(X) = ax+b

at x = 0, g(x) = 42000, the function becomes;

g(X) = ax+b

42000 = a(0)+b

42000 = 0+b

b = 42000

at x = 1, g(x) = 56256

56256 = a(1) + b

56256 = a+b

a = 56256 -b

a = 56256 - 42000

a = 14,256

To get the average family income in 1997, wee need to calculate g(x) at when x = 5, since the number of years between 1992 and 1997 is 5years.

g(x) = ax+b

g(5) = 14256(5) + 42000

g(5) = 71,280+42000

g(5) = 113,280

Hence the average family income in 1997 is 113,280