They had 23 and 38 water bottles on day 2 and day 4 respectively. Also, there will be 68 water bottles on day 7.
Step-by-step explanation
Suppose, the equation representing the number of bottles is
, where
is the number of days.
There are 17 water bottles on day 1, 30 water bottles on day 3 and 47 water bottles on day 5
So, the three points in the form of (x, y) are: (1, 17) , (3, 30) and (5, 47)
Plugging these three points into the above equation, we will get .....

Subtracting equation (1) from equation (2) , we will get .....

Subtracting equation (2) from equation (3) , we will get .....

Now, subtracting equation (4) from equation (5) , we will get ......

Substituting this
into equation (4) ........

Again, substituting
and
into equation (1) , we will get ......

So, the equation will be now:

For finding the number of bottles on day 2 , day 4 and day 7 , we need to plug
respectively into the above equation.
For
,

For
,

For
,

So, they had 23 water bottles on day 2 and 38 water bottles on day 4
Also, there will be 68 water bottles on day 7