Answer
a. $9\%$.
b. increasing, $1\%$.
Work Step by Step
a. Given $\frac{du}{dt}=0.04u$ and $\frac{dv}{dt}=0.05v$, we have $\frac{dy}{dt}=u\frac{dv}{dt}+v\frac{du}{dt}=0.05uv+0.04uv=0.09uv=0.09y$ which means that the rate of growth of the total production is $9\%$.
b. In this case, $\frac{du}{dt}=-0.02u$ and $\frac{dv}{dt}=0.03v$, we have $\frac{dy}{dt}=u\frac{dv}{dt}+v\frac{du}{dt}=0.03uv-0.02uv=0.01uv=0.01y$
which means that the total production is increasing at a rate of $1\%$.
