Exponential or Inversely Proportional?

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don'tTRIP.
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#1
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#1
Quick question, how would you distinguish between these 2 types of graphs? Haven't got any examples; sorry for being so vague
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Stonebridge
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#2
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#2
Inversely proportional is a straight line with negative gradient. (See my correction edit below)
Exponential is curved either upwards or downwards depending on whether it's a positive or negative exponential.

The one below is a negative exponential for the temperature of an object that is cooling down.

Image

Edit.
My apologies rushing the answers tonight. Inversely prop (eg y=1/x) is not a straight line. It looks very similar to the negative exponential.
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bmqib
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#3
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#3
(Original post by Stonebridge)
Inversely proportional is a straight line with negative gradient.
Exponential is curved either upwards or downwards depending on whether it's a positive or negative exponential.

The one below is a negative exponential for the temperature of an object that is cooling down.

Image
Doesn't inversely proportional imply y=1/x, so x can never be zero and vice versa? So we have a curve that looks like a negative exponential curve except it's not? Unless I am plotting y against 1/x maybe
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Stonebridge
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#4
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(Original post by bmqib)
Doesn't inversely proportional imply y=1/x, so x can never be zero and vice versa? So we have a curve that looks like a negative exponential curve except it's not? Unless I am plotting y against 1/x maybe
Oops sorry. My mistake rushing the answers tonight.
Yes, inversely proportional is prop to 1/x and is not a straight line.
I was thinking for some reason of negative gradients.
And yes, the curve looks like a negative exponential like the one I posted.
With the difference being posted by the poster below.
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+ polarity -
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#5
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#5
Erm... an exponential will go through (0,[1 or whatever e is multiplied by]), while 1/x is not defined at x = 0.
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Stonebridge
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#6
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#6
(Original post by + polarity -)
Erm... an exponential will go through (0,[1 or whatever e is multiplied by]), while 1/x is not defined at x = 0.
Yes.
Like this

Image
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aperk64
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#7
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#7
While that is the case for an exponential relationship, what about an exponential decay relationship? how would someone be able to determine the difference between these two types of graphs
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Stonebridge
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#8
Report 2 years ago
#8
Wow. This thread was started 7 years ago and I have just returned to TSR after 5 years away.
If you are asking about the difference between an inverse square and an exponential decay, the simplest visual test, is to look at the value at x=0.
Normally an exponential delay curve starts at some definite point on the y axis and then falls gradually to zero along the x or (very often) the time axis.
An inverse square curve is undefined at x=0 because 1 divided zero is 'infinity'. So it would not have that defined starting point on that vertical y axis as the exponential decay curve would. In fact, it would not touch the y axis at all.

Let me know if this is helpful.
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