Function notation word problem: bank

Arjun opened up a savings account last year and put an initial sum in it let M of T denote the account balance M measured in dollars T days since it was opened what does the statement M of 30 minus M of zero equaling a hundred mean so before I even look at the choices let's think of it this means when you input T equals 30 into your function you're going to get M of 30 so let me make that clear so if you say T is equal to 30 you input that into your function M you are going to get you are going to get M of 30 so one way to think about it is this is the account balance 30 days since it was open this is when T is equal to 30 this is the account balance after 30 days let me write that down balance balance after 30 days now by the same logic this right over here this is when we put T when we set T equals zero this is the balance after zero days or you could say this is the initial balance initial initial balance so what they're doing they're taking our balance after 30 days and from that they're subtracting the initial balance and they're saying that that's equal hunt equal to 100 so there's a couple of ways you can interpret this and I haven't even looked at these choices yet we'll see if any of these match up you could say that your balance after 30 days is $100 more than the initial balance or another way to think about it is you've added $100 in the first 30 days those are both legitimate ways to think about it now let's see which of these choices are consistent with that 30 days after it was opened the balance of Argent's account was equal to a hundred no that's not what that's saying this statement right over here that the balance 30 days after opening this statement right over here this would be equivalent this is equivalent to saying that M of 30 this is the balance after 30 30 days after was open is equal to 100 that's not what they tell us here they tell us that the difference between the balance after 30 days and the initial balance of that is a hundred so we can rule that one out had the initial amount of money in his account 30 days after he opened it so if he had the same amount if he had the initial amount let me write this down so had the initial amount of money the image the initial amount of money is M of 0 so they're saying he had the initial amount of money in his account 30 days after he opened it well the amount that he has in his account 30 days after he opened it is M of 30 so these are the same amounts of money then this in order to be consistent with this you would have had an equation like this M of 0 the initial amount is equal to the amount after 30 days that's not what they told us over here so we can rule that out and then finally we have the choice Arjun made a profit over of $100 over the first 30 days since the account was opened and that seems reasonable that his balance is $100 higher the difference between if you take his initial balance and subtract it from his balance after 30 days it's a hundred that this right over here is a hundred higher than his initial balance so it makes sense and maybe he got that profit I don't know it's an interest or something else that he got in his bank account over the first 30 days