trolling motor question

Think of your battery as a fuel tank (within reason).  The larger capacity of your battery, the longer it will run. If you run the motor at slower speeds, it will run longer.  Trolling motors, generally, are power hogs when run at full throttle.  Most will reach most of their peak performance at about 75% and give you about the best distance vs. power consumption.

This is what I've learned about trolling motors.
If you do not have a variable speed model (digital maximizer) and have a 5 speed model, choosing a slower speed such a 1 (low speed) will not save you much battery capacity.  To slow a five speed model full current is diverted through a resistance coil to reduce the voltage to the motor thus slowing the speed.  At 5 (high speed) full current is allowed to power the motor providing maximum rpm. 
You can pick up a PWM 30 amp controller and wire it in the lid of the Minn Kota 30 or buy the MK endure max. This will allow you to extend your time on the water.
The way the PWM (Pulse Width Modulation) works is it converts the voltage into a signal of on-off pulses and gives a linear power output.  The slower the speed, more battery life is saved. 
I've installed a few in a couple of trolling motors and they work great.  I'm planning on doing one for CK but its out of stock as of now.  I'll post a DIY on it when its in.

Uh, yeah ... What he said 

I know of less than 3 people on here who use a trolling motor on their kayak.

I always wondered how common this is. I don't recall ever seeing a motorized yak on saltwater. But, I often chat with people on the dock after fishing, and several times I've heard stories about motorized kayaks. It seems they make a lasting impression...

Also,
If your battery is rated in CCA, you have a marine battery, but not necessarily a deep cycle. You need a deep cycle to get any time out of it.
A "marine" battery just means the case is built for the Marine environment. A "deep cycle" is built to drain slower and continue to be recharged.

Once you register a yak, or boat, they cannot be "unregistered" so you are stuck paying that every two years till the kayak is sold or destroyed.  Unlike a car, you cannot non-op the registration.

Also you will need to affix registration (CF) numbers/letters to each side of the hull....

Also,
If your battery is rated in CCA, you have a marine battery, but not necessarily a deep cycle. You need a deep cycle to get any time out of it.
A "marine" battery just means the case is built for the Marine environment. A "deep cycle" is built to drain slower and continue to be recharged.

That is an EXCELLENT point!  Another is "quality" of the battery, battery charger source/type/quality, storage habits of a battery & a number of other factors can weigh into the overall quality of any 12v electrical system.  One other thing that becomes overlooked is corrosion.  Having been in the marine industry, I saw way too many Freshwater motors try & be returned after having been used (and not properly maintained) in a Saltwater environment.  There is a difference in the quality & construction of the motors; hence the reason manufacturers offer a FW vs SW series motor.