Economics The median family income is the middle income half

Economics The median family income is the \"middle income\" -half the families have this income or more, and half have a lesser income. The median family income can be approximated by f(x) = 22, 751 + 8217 ln(x + 1), where x = 0 corresponds to the year 1990. (Data from: U.S. Census Bureau.) What is the median income in the years 2000 and 2010? If this model remains accurate, when will the median income reach $52,000?

Solution

f(x)= 22751 + 8217ln(x +1)

a) in year 2000 ;x = 10

f(10) = 22751 + 8217ln(11)

= 42454.51

year 2010 ;x = 20

f(20) = 22751 + 8217 ln(21)

= 47767.84

b) f(x) = 52000 , find x:

52000 = 22751 + 8217 ln(x+1)

3.559 = ln(x+1)

35.128 = x +1

x = 34.128

year 2025