utv
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what does this mean on the exponential graphs. I've tried to research it and can't find anything. any help much appreciated

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username4426374
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Nice blurry picture which are shown the wrong way.
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utv
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sorry I will correct now
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utv
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areas highlighted in orange I don't understand what it means. can anyone explain in simple terms
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mqb2766
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(Original post by utv)
what does this mean on the exponential graphs. I've tried to research it and can't find anything. any help much appreciated

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Typing the question would have helped in this case.

Simple example is radioactive decay, every xxx years (half life), the activity decays by 1/2. The gradient or rate must slow down as the activity decreases
https://en.wikipedia.org/wiki/Exponential_decay

Obviously, you can exponential growth as well. Bank interest. The more money you have, the greater the amount is credited to your account. The interest rate (exponent) stays the same.
https://en.wikipedia.org/wiki/Exponential_growth

Maths speak
y = Ae^(kt)
then
dy/dt = kAe^(kt) = ky
as y increases or decreases, the rate of change increases or decreases.
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username4426374
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Is this A-level?
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halsx11
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No GCSE I don’t get it either
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utv
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oh ok. so the rate of change is directly proportional to y? can you work out the gradient by this?

and no it's as level not GCSE. nothing to worry about
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mqb2766
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(Original post by utv)
oh ok. so the rate of change is directly proportional to y? can you work out the gradient by this?

and no it's as level not GCSE. nothing to worry about
You have
dy/dt = ky
which you can solve by splitting it up as
(1/y) dy = k dt
integrate to get
ln(y) - ln(A) = kt
take inverse logs (exponential)
y = Ae^kt
A is the initial value y(0). So they're basically the same thing saying:
* y(t) is an exponential
* the derivative (rate of change) is proportional to its value.
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halsx11
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(Original post by utv)
oh ok. so the rate of change is directly proportional to y? can you work out the gradient by this?

and no it's as level not GCSE. nothing to worry about
It’s GCSE in on my syllabus and I’m learning it as well! GCSEs have got harder and they have got A-Level topics inside it as well! Idk why AQA has done this!
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carl fringos!
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Hi,
not really sure about this but if dy/dx gives the slope of some function of x say x^2 or x+2 or e^x, and y gives the value of that function, so y=x^2 or y=x+2 or y=e^x, then we are after a function where the slope of the function is proportional to the value of the function.

This can be written as dy/dx=ky, where k is the constant of proportionality.

This equation is talking about some function of x with the property that the value of that function is proportional to the value of the slope. So if you double the value of the function, you double the slope. And im not sure but exponentials might have this property which might explain the paragraph.
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utv
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this makes sense. if that is the case.is it true. thank you for all your responses. I can't rep all of you as I've rep you so much because you help constantly. much appreciated
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CraigFowler
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(Original post by utv)
what does this mean on the exponential graphs. I've tried to research it and can't find anything. any help much appreciated

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Hopefully in plain English

If y=e^x then dy/dx = e^x

This is a standard differential, that the function is the same as the differential equation.

Does that make sense?
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