5. The price of a commodity is p dollars and the quantity supplied is x units, where
. Find the rate of change of the quantity supplied with respect to time t (measured in months) when the price is $4 and is increasing at the rate of 80 cents per month.
Solution: Using the chain rule we find that
From the given equation, and using the Chain Rule again, we find
Hence,
Butand, which means that
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