Question

# The gross annual earnings of a certain company were $A(t)=0.1 t^2+10 t+20$ thousand dollars $t$ years after its formation in 2004.a. At what rate were the gross annual earnings of the company growing with respect to time in 2008 ?b. At what percentage rate were the gross annual earnings growing with respect to time in 2008?

Solution

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The given function is $A(t)=0.1t^2+10t+20$ Hence the derivative is

\begin{align} \frac{dA}{dt}&=0.2t+10 \end{align}

In the year 2004, the rate of change is

\begin{align} \frac{dA}{dt}\bigg|_{t=4}&=10.8 \end{align}

i.e., 10,800 dollar per year.