based on data from 1995 to 1999, the average annual warnings in the paper and allied products manufacturing industry may be maodeled by

E(t)=1335t+39408 dollars per employee
and the average number of emplyees in the same industry cab be modeled by
N(t)=t^3+5.571t^2-12.29t+684.9 thousand emplyees
where t is the number of years since 1995
in 1999, at what rate was employers spending on paper and allied products manufacturing industry emplyee earning increasing

I have no idea what you are saying.

Why are there warnings in the paper industry?

Hmmm. Let's say "earnings" instead of "warnings" and all becomes clear.

E(t) = earnings/employee

earnings = earnings/employee * employees

So, we want P(t) = E(t)*N(t) for total earnings

P' = E'N + EN'

go for it. These are just simple polynomials.

Actually, num of employees = 1000*N

To find the rate at which employers' spending on paper and allied products manufacturing industry employee earnings was increasing in 1999, we need to calculate the derivative of the equation E(t) = 1335t + 39408 with respect to t.

The derivative of E(t) will give us the rate of change of E(t) with respect to t, which represents the rate at which employers' spending on employee earnings is increasing.

Taking the derivative of E(t) = 1335t + 39408 with respect to t:

dE/dt = 1335

Since the derivative is constant (1335), it means that the rate at which employers' spending on employee earnings is increasing is constant.

Therefore, in 1999, the rate at which employers' spending on paper and allied products manufacturing industry employee earnings was increasing was 1335 dollars per year.