Hi! Logically, we think concrete cures by drying - Not True! Concrete cures/gains strength by hydration. That is, a chemical process caused by the interraction of water and the portland cement (the "active ingredient" of concrete.)
This means that if wet concrete is allowed to dry too quickly (before full hydration) it will be weaker than if properly cured. A slab should be kept damp through the curing stage. Concrete guys will tell you to sprinkle with the garden hose 3 times a day. If you do that with a slab sitting in the sun, the surface dries out between "sprinkling." In that case you've wasted your time with the hose.
The best way to cure is to keep the surface damp CONTINUOUSLY through the cure. Sprinkle the surface then cover it with plastic to hold the moisture in until you sprinkle again (3 times a day is good.) You can up the odds that no portion of the surface will dry out by spreading a layer of straw, burlap, etc. Wet that down then cover with plastic.
How long? Concrete continues to harden for a period of years. However, properly cured (see above) it will achieve 50% of its strength in 3 days. It will achieve 80% of its strength in 7 days. At that point the process slow greatly. You can set the tub after 3 - 4 days but you'll have a significantly stronger slab if you wait & cure as outlined above for 7 days.
I'm digging right now for a 6" slab that will be re-inforced w/rebar (yes, that's overkill per most tub manufacturers.) When I pour, as soon as the surface is "finished" I'll cover with burlap/sprinkle/plastic and keep it that way for 7 days. I'll let it sit "open" for 1 day then land the tub. BTW, the reason I'm going "overkill" (6"w/steel reinf.) is because a slab "floats" when portions of the ground freeze. The stronger the slab, the better chance it will float as a single plane rather than crack. The re-inforcing rods don't prevent cracks but help keep the slab in a single plane after cracks occur. (Think about sidewalks that crack, then one side of the crack lifts and the 2 sections are out of plane.)
File this all under FWIW. You can do your own research by asking these questions of your concrete guy or go to the library - lots of "how to" books that will tell you all of the above. Good luck to all, gotta go dig!