The rate of growth, in dollars per year, of the net worth, f(t), of a company is given by f′(t)=1850+(−4)t^2, where t is measured in years since 1992. If the company is worth $30000 in 1992, what is it worth in 2000?
Value in 2000:
f'(t) = -4t^2 + 1850
f(t) = -4/3 t^3 + 1850t + C
since f(0) = 30,000, C = 30000 and
f(t) = -4/3 t^3 + 1850t + 30000
Now find f(8)
I gotta say, though, that I suspect a typo, since this company will start losing value in a big way at t=20