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?

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?

Quizlet Admin · Accepted Answer

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.

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