That seems a little large to me, but maybe if you use a lot of water. Here are some calculations.
Current hardness in grains is 7. Since we don't know at the moment, I'll add 0.2 for iron as a guess. If there is no iron that's great but it's just to be on the safe side. That adds 0.2 * 4 or 0.8. So your compensates hardness is 7.8, let's just call it 8 to be safe.
4 people times 70 gallons per day gives you 280 gallons per day. Just for safeness, let's add 20 gallons to arrive at 300 gallons per day.
Now to get how much hardness you need to remove per day, multiply the gallons per day needed times your compensated hardness. So that is 300*8, which is 2400.
If you regenerate once per week, you multiply 2400*7, giving you 16,800 total grains capacity needed.
For efficient salt use, you need to run your softener at around 70% of it's rated size. A 1 cuft softener with a nominal size of 32K run at 70% will give you a capacity of 22,400. plenty of capacity for your needs of 16,800.
Now if your hardness goes up, all this will need to be redone.
G