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# exponential growth and decrease Watch

1. Hi guys,
i have a number of readings from a voltmeter which are decreasing exponentially and the question asked me to show if the voltmeter reading is decreasing exponentially but I'm not sure how to do that. I'm aware that for a exponential change the quantity changes by a fixed proportion in equal intervals of time but when it comes to apply in in a question i get stuck
any help would be much appreciated
2. To show an exponential relationship, you take "half life" readings. At a certain time x, take a reading y. Then at time 2x, take a reading of y and you should get around 2y (or 1/2 y if it's an exponential decrease). Repeat this 3 times at 3 different points (2 on some syllabi) to show an exponential relationship
3. (Original post by Student403)
To show an exponential relationship, you take "half life" readings. At a certain time x, take a reading y. Then at time 2x, take a reading of y and you should get around 2y (or 1/2 y if it's an exponential decrease). Repeat this 3 times at 3 different points (2 on some syllabi) to show an exponential relationship
so for instance if i have a reading of 5.5v in 2 seconds , in time 4 seconds i should get 11v for exponential growth to be proved and in time 4 seconds i should get 2.75V if the exponential is decreasing is this right?
4. (Original post by Alen.m)
so for instance if i have a reading of 5.5v in 2 seconds , in time 4 seconds i should get 11v for exponential growth to be proved and in time 4 seconds i should get 2.75V if the exponential is decreasing is this right?
exactly - how did it work out?
5. (Original post by Student403)
exactly - how did it work out?
basically the variable changes in a time proportion to the variable itself
6. (Original post by Alen.m)
basically the variable changes in a time proportion to the variable itself
Yeah I know I mean did it work for you?
7. (Original post by Student403)
Yeah I know I mean did it work for you?
oh that well to be honest i came up with a bunch of random numbers just to understand the definition of exponential growth and decrease in them which i did but i didn't actually do the experiment but once i understand the definition of it i can apply it to the readings and questions i guess
8. (Original post by Alen.m)
oh that well to be honest i came up with a bunch of random numbers just to understand the definition of exponential growth and decrease in them which i did but i didn't actually do the experiment but once i understand the definition of it i can apply it to the readings and questions i guess
Ah okay

Remember another way to prove y has an exponential relationship with x is to plot lny against x and see if you get a straight line. That commonly comes up in exams too
9. (Original post by Student403)
Ah okay

Remember another way to prove y has an exponential relationship with x is to plot lny against x and see if you get a straight line. That commonly comes up in exams too
do you mean i should calculate In of each value of Y and plot against graph t to see if it gives me a straight line? so the points basically are the reading except from calculating In for y values?
10. (Original post by Alen.m)
do you mean i should calculate In of each value of Y and plot against graph t to see if it gives me a straight line? so the points basically are the reading except from calculating In for y values?
yes
11. (Original post by Student403)
yes
even if the exponential decay was decreasing, the graph of InY against t should give me a straight line through origin or just a straight line?
12. (Original post by Alen.m)
even if the exponential decay was decreasing, the graph of InY against t should give me a straight line through origin or just a straight line?
For decay you'd get a straight line with negative gradient, so that couldn't go through the origin anyway.

For growth it's possible but not a guarantee or anything.
13. (Original post by Student403)
For decay you'd get a straight line with negative gradient, so that couldn't go through the origin anyway.

For growth it's possible but not a guarantee or anything.
thanks mate
14. (Original post by Student403)
For decay you'd get a straight line with negative gradient, so that couldn't go through the origin anyway.

For growth it's possible but not a guarantee or anything.
i just noticed that if you put zero as one of Y values and try to calculate In of it it'll be undefined so the graph of InY against x wouldnt go through the origin at all hence the simple exponential graphs wouldn't go through the origin at all in any cases even in a simple exponential graph of y against x for a exponential relationship between two variables . do you think this conclusion is right?
15. (Original post by Alen.m)
i just noticed that if you put zero as one of Y values and try to calculate In of it it'll be undefined so the graph of InY against x wouldnt go through the origin at all hence the simple exponential graphs wouldn't go through the origin at all in any cases even in a simple exponential graph of y against x for a exponential relationship between two variables . do you think this conclusion is right?
I don't agree.

What about when your y variable is 1 at x = 0?
16. (Original post by Student403)
I don't agree.

What about when your y variable is 1 at x = 0?
you're right--how about if we say the graph wouldn't go through the origin except from when you have y=1 and x=0 for as two different readings for two different variables
17. (Original post by Alen.m)
you're right--how about if we say the graph wouldn't go through the origin except from when you have y=1 and x=0 for as two different readings for two different variables
Correct. The only time lny = 0 is when y = 1

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