write a differential equation for the following.

Question

a cell starts at a volume of 400m^3 and gains volume at a rate of 3m^3/s

Answer 1

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 ...