The rate of growth, in dollars per year, of the net worth, f(t), of a company is given by f′(t)=2160+(−12)t^2, where t is measured in years since 1990. If the company is worth $30000 in 1990, what is it worth in 2000?

Question

The rate of growth, in dollars per year, of the net worth, f(t), of a company is given by f′(t)=2160+(−12)t^2, where t is measured in years since 1990. If the company is worth $30000 in 1990, what is it worth in 2000?

Value in 2000:

Answer 1

f′(t)=2160+(−12)t^2

so f(t) = 2160t - 4t^3 + c
so when t = 0 , (1990), f(0) = 0 -4 + c = 30000
c = 30004

so we have f(t) = 2160t - 4t^3 + 30004
in 2000 ----> t = 10
f(10) = 2160(10) - 4(1000) + 30004
= 47,604