Here's how you think about it...
Let us call the newborn weight x. In this example, X0 = 0.06 gm.
After day 1, the weight will increase by 10%, i.e.by 0.1X0
So, weight after day 1,
X1 = X0.+0.1X0
= X0.(1 +0.1) ------- (1)
Weight after day 2, X2 = X1.(1+0.1)
Substitute for X1 from equation (1)
X2 = X0.(1 +0.1)2
Similarly, you can calculate Weight after day 3,
X3 = X2 + 0.1X2
Or, X3 = X0.(1 +0.1)3
Now you can see the pattern developing.. You can generalize this to
Weight after day 'n'
Xn = X0.(1 +0.1)n
In a six week period there are 42 days. So you are asked to calculate the weight after 42 days. Using your calculator, and knowing X0 = 0.06 gm, you can estimate the weight to be approx 3.28 gm