Question

a government considers a single person as living in poverty if his or her income falls below the official poverty level, which is adjusted every year for inflation. the function that models the poverty threshold for the years 1987 - 2008 is ( f(x)=-3140.4 + 4055.2ln x ) dollars, where ( x ) is the number of years after 1980.
a. what does this model give as the poverty threshold in 2017? in 2020?
b. is this function increasing or decreasing?
c. graph the function ( -3140.4 + 4055.2ln x ) for ( x = 5 ) to ( x = 40 ).
a. the threshold will be about ( $ ) in 2017.
(round to the nearest dollar as needed.)

Explanation:

Step1: Calculate \(x\) for 2017

\(x = 2017 - 1980=37\)

Step2: Substitute \(x = 37\) into \(f(x)\)

\(f(37)=-3140.4 + 4055.2\ln(37)\)
First, calculate \(\ln(37)\approx3.6109\)
Then \(f(37)=-3140.4+4055.2\times3.6109\)
\(f(37)=-3140.4 + 14640.9717\)
\(f(37)\approx11501\)

Answer:

\(11501\)