If for every month the balance increase by 1%, this means that each month you will apply 1% to the amount it is in the balance.
To apply once, we can take one 1% of the amount and add it to that amount. So, this is the same as taking 101% of the amount.
To take 101% of the amount, you can multiply by 1.01.
So, with an initial amount of $750, after one month, you wil multiply it by 1.01:
[tex]B(1)=750\cdot1.01[/tex]After one more month, you will multiply this new amount by 1.01, so you sill get:
[tex]B(2)=750\cdot1.01\cdot1.01[/tex]If you do this for "t" months, you will multiply by 1.01 "t" times, which is the same as multiplying by 1.01 to power of "t":
[tex]B(t)=750\cdot1.01\cdot1.01\cdot1.01\ldots(x\, times)=750(1.01)^t[/tex]So, the formula is:
[tex]B(t)=750(1.01)^t[/tex]