Gradient problem

W

WilliamPat

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Thanks both of you for your answers!!!!


Wlliam Patterson
 
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WilliamPat said:
A video clip is posted on the internet and receives a high number of views.Someone looks at the number of views for the first year that this clip is online.He says that the total number of views can be modelled by the equation y=1500x where x is the number of days since the clip was posted and y is the total number of views.


i) Write down the gradient of the straight line represented by the equation y=1500x
What does this measure in the practical situation being modelled?

i know that the gradient is 1500 but i dont understand what does it measure in the practical situation being modelled.


Thanks


Wlliam Patterson
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One of the things which helps with doing 'real life' problems is what is called unit analysis. What that means is that, for 'real life' problems, numbers and variables have units (types) associated with them. In the case here the units of y is views and the units of x is days so we can write the equation as
y views = 1500 (units of 1500) * x days
The arithmetic still works with units so we can divided both sides by x days to get
\(\displaystyle \frac{y\space views}{x\space days}\) = 1500 (units of 1500)
So
\(\displaystyle \frac{y}{x}\) \(\displaystyle \frac{views}{days}\) = 1500 (units of 1500)
and 1500 represents (average) views per day.

As an aside, we can also note that we can divide both sides of the above equation by views/day and the whole equation is unit-less AND is usually what we see in math books and problems. So, in a formal sense, if one is going to talk about properties of the formula you have to decide from the context of the question which is meant: Is this a problem with (unstated) units or does it represent a unit-less problem. This can become important in some of the higher mathematics.
 
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Ishuda said:
One of the things which helps with doing 'real life' problems is what is called unit analysis. What that means is that, for 'real life' problems, numbers and variables have units (types) associated with them. In the case here the units of y is views and the units of x is days so we can write the equation as
y views = 1500 (units of 1500) * x days
The arithmetic still works with units so we can divided both sides by x days to get
\(\displaystyle \frac{y\space views}{x\space days}\) = 1500 (units of 1500)
So
\(\displaystyle \frac{y}{x}\) \(\displaystyle \frac{views}{days}\) = 1500 (units of 1500)
and 1500 represents (average) views per day.

As an aside, we can also note that we can divide both sides of the above equation by views/day and the whole equation is unit-less AND is usually what we see in math books and problems. So, in a formal sense, if one is going to talk about properties of the formula you have to decide from the context of the question which is meant: Is this a problem with (unstated) units or does it represent a unit-less problem. This can become important in some of the higher mathematics.
Click to expand...


So the gradient represents average views per day?
 
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