00:01
In order to solve this problem, we need to examine the relationship between two things.
00:05
So an x and a y or an independent and independent variable.
00:09
So that's what we're going to do today.
00:11
So let's start with problem a.
00:14
So a is looking at the temperature of a bowl of soup as a function of time.
00:20
So the two things that we are looking at, the relationship between is going to be temperature of the bowl of soup and time.
00:28
So all we need to do is figure out what happens to the other and when we affect it and when we manipulate it.
00:39
So looking at temperature and time, think about it like this.
00:44
If we have a hot bowl of soup and time goes on and time is increasing in 20 minutes compared to an hour, is that soup going to be warmer or colder? it's going to be colder because it had more times to cool it down.
01:01
So this will be true for any kind of hot thing, right? so the more time you leave it out in an environment that's cooler than it, it will get cooler.
01:15
The temperature will be lowered.
01:16
So the graph we can show for this, showing that time is on the x -axis and temperature is on the y, would look something like this.
01:29
The reason that, so we know that why it's decreasing, right? because time is increasing and temperature is getting lower.
01:36
However, the reason it's not actually touching either of these axes is that the time could be zero, but the temperature could.
01:47
It's never going to be cold enough that the temperature of the soup gets that low.
01:51
So we don't assume that, so we kind of keep it like this.
01:56
Also, the reason that it's exponentially and not linear, like a straight line like that, is because there's no exact, i guess, linear relationship between, if it's, if 20 minutes pass, then it will exactly be at this temperature.
02:13
There's no constant and there's no, it's not proportional to each other.
02:19
So that's why it looks like that.
02:22
Now on to b.
02:24
So b is asking us to find the relationship between the number of hours for daylight.
02:31
So hours of daylight.
02:31
So hours of day and it's from winter to summer per year and it's for two years so we'll say time so if you so looking at hours for daylight we know that it increases from winter to summer every year so when it goes from winter to summer it's an increase but we're looking at it for two years so that's going to have to happen again so although it's increasing from winter to summer here it then we have to go back down down to then increase back here for the second year.
03:19
So it's kind of going up and down.
03:21
So that would give us enough evidence to draw.
03:26
We're gonna put time on x and let's just put daylight as the y.
03:33
It would look something like this, kind of going up and down as time moves on.
03:39
So time is pretty steady and constant, but the daylight is what, um, is bouncing up and down.
03:48
Then on to c.
03:49
The c is talking about the population of florida over time.
03:53
So let's put population.
03:57
The fact they mentioned florida does not affect this problem...