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## Interpreting function notation

# Function notation word problem: beach

CCSS.Math:

## Video transcript

Let P of t denote the number of people P at the Copacabana beach in Rio de
Janeiro, t hours past midnight on a specific day.
What does the statement P of 5 less than P of 9 mean? So before I
read these, let's think about this. So this is the number of people five
hours past midnight on a specific day. So this is saying that the number of people
five hours past midnight is less than the number of people nine
hours past midnight at Copacabana beach. So the number of people
five hours past midnight is less than the number people nine
hours past midnight. Let's get into these choices. The time at which there were five people
at the beach is earlier than the time there were nine
people. Who know? -- the five and the nine aren't
the number of people This is the time. This is the input into
the function. The input into the function is time. This
gives people as a function of time. You give a time. You give a time. This function P, it outputs P of t, which is equal to the number of
people number of people on the beach at time, at time t. So this five -- this is the input. This is
the time five hours after I shouldn't say time t. I guess you
could say a.m. time -- t hours past midnight at t hours past midnight, hours past past midnight. midnight. So we can definitely rule this out. This
isn't talking about five people or nine people. This is talking about five hours after midnight is input and
how many people we have five hours after midnight is how many people we have nine hours
after midnight. 5 a.m. is an earlier time the 9 a.m. Well, that is a true statement but that's not
what this statement is saying. It's not -- this isn't giving us
information which is no from, I guess, how we think about time or how
we measure time. the 5 a.m. is earlier than 9 a.m. but
that's not what this statement is trying to say. So rule that out. There were more people at the beach at
9 a.m. So to be clear, people at the beach at
9 a.m. that's that right over here -- than there were -- than there were at 5 a.m. -- than there were
at 5 a.m. Well, that's right over there. And we see -- we see this quantity here
is greater than those magenta quantity is indeed greater than this green quantity.
The green quantity is less than the magenta quantity, so we
would definitely pick that one.