The rate of change of the projected total assets (in constant 2005 dollars) in the Social Security trust fund for the years 2000 through 2040 can be modeled as

f(x) =0.365x²0.295x+ 176.32 where output is measured in billion dollars per year andxis the number of years after 2000.

a) When will the trust fund assets be declining? (Round your answers to the nearest integer.)

The projected total assets in the Social Security trust fund are declining from the year (blank) through the year(blank).

b) When will the amount in the trust fund be greatest? (Round your answer to three decimal places.)

The amount in the trust fund will be at a maximum after(blank) years which will occur in the year(blank).

(c) Use a limit of sums to estimate the area of the region between the graph offand thex-axis fromx= 0tox= 40.(Round your answer to one decimal place.)

$(blank) billion

Please fill in the blanks and state answer clearly.