91Ó°ÊÓ

Change to exponential form. $$\log _{36} 6=\frac{1}{2}$$

A company estimates its profit \(P\) per item on a certain item as a function of the number \(x\) of items produced. The equation is \\[P=4 \ln \left(2+x^{2}+0.01 x^{3}\right)\\] for \(10 \leq x \leq 10,000 .\) Use differentials to estimate the change in \(P\) as \(x\) changes from 2000 to 2100.

Use your calculator. The voltage \(V\) (in volts) across a certain capacitor at any time \(t\) (in seconds is given by \(V=e^{-0.004 t}\). Find \(V\) at \(t=7\) \(\mathrm{s}\).

A particle moves according to the parametric equations \(x=t+\cos t, y\) \(=\cos ^{2} t .\) Find the velocity vector for \(t=1\).