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# Function notation word problem: bank

CCSS Math: HSF.IF.A.2

## Video transcript

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 0 equalling a hundred mean?
Before I look at the choices, let's think about what 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're going to get -- you're going to
get M of 30. So one way to think about it
is -- This is the account balance 30 days
since it was opened. This is when t is equal to 30. This is the account balance
after 30 days Let's write that down. Balance -- balance after 30 days. Now, by the same logic, this
right over here this is when we put t where we said t equals 0. This is the balance
after 0 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 equal to 100. So there's a couple 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 a hundred dollars more than the initial balance. Or another way to think about is
you added a hundred dollars in the first 30 days. Those are both legitimate ways to think
about it. I'll see which of these choices are consistent with that. 30 days after it was
opened, the balance of Arjun's account was equal to 100. No, that's not what that's
saying. This statement right over here -- 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
days after it was opened -- 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 -- that's a hundred. So we can rule that one out. Arjan 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 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 had 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 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. We can rule that out. And then finally we have the choice Arjan made a profit
over a hundred dollars over the first 30 days since the account
was opened. That seems reasonable that his balance
is a hundred dollars higher. The difference between -- if you take the initial
balance and subtract it from his balance after 30 days, it's a hundred. And this right over here is a
hundred higher than his initial balance. So it makes sense that maybe he got the
profit out of an interest or something else that he got in his bank account over the
first 30 days.