write a differential equation for the following.
a cell starts at a volume of 400m^3 and gains volume at a rate of 3m^3/s
Uh, how about
v = 400 + 3t
where t is the time in seconds
You want volume in m3. Keep the units as you go along, and you can see what has to be used:
v = 400m3 + 3m3/s * s
That's why you multiply by time, to change rate to volume. You can only add like units: volume.
I also assume you mean µm or something like that. Most cells don't come in meter sizes ...