# chain rule

• Dec 15th 2006, 10:45 PM
frozenflames
chain rule
The average commission c (in dollars) per trade earned by the Charles Schwab Corporation decreased as more of its customers traded online according to the formula

C(u) = 100u^2 - 160 u +110 dollars per trade (u = th efraction of trades done online)

During that time, the fraction of online trades increased according to

u(t) = .42 + .02t (t = months since January 1, 1998)

Question 1. Use the chain to estimate the rate of change of average commission per trade at the beginning of September 1998. Be sure to specify the units!

• Dec 16th 2006, 10:57 AM
CaptainBlack
Quote:

Originally Posted by frozenflames
The average commission c (in dollars) per trade earned by the Charles Schwab Corporation decreased as more of its customers traded online according to the formula

C(u) = 100u^2 - 160 u +110 dollars per trade (u = th efraction of trades done online)

During that time, the fraction of online trades increased according to

u(t) = .42 + .02t (t = months since January 1, 1998)

Question 1. Use the chain to estimate the rate of change of average commission per trade at the beginning of September 1998. Be sure to specify the units!

$\displaystyle \frac{dC}{dt}=\frac{dC}{du}\,\frac{du}{dt}=(200u-160)(0.02)$
Now the $\displaystyle t$ corresponding to the 1st of September is 8 months,
so $\displaystyle u(8)=0.58$, so:
$\displaystyle \frac{dC}{dt}(t=8)=(200\times 8-160)(0.02)=28.8 \mbox{ dollars per trade per month}$