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C3 Exponentials

Question: (need help on part d):



Need help on part d). I sketched the correct graph but didn't have an asymptote. Can anyone explain why in the graph below, there is an asymptote of N = 100?

Answer from textbook:

Spoiler

Original post by Inevitable
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Consider graph transformation of N=et N = e^t .

Hope this helps. :smile:
Reply 2
Original post by lazy_fish
Consider graph transformation of N=et N = e^t .

Hope this helps. :smile:


Oh, I see. The transformation is a stretch by scale factor 50 parallel to y-axis giving the coordinates (0, 50) where it cuts the y-axis with an asymptote of y = 0. Then a shift of 100 units upwards giving coordinates (0, 150) with an asymptote of y = 100.
Original post by Inevitable
Oh, I see. The transformation is a stretch by scale factor 50 parallel to y-axis giving the coordinates (0, 50) where it cuts the y-axis with an asymptote of y = 0. Then a shift of 100 units upwards giving coordinates (0, 150) with an asymptote of y = 100.


N =100 is only an asymptote if you extend the graph for negative values of t.
Reply 4
Original post by brianeverit
N =100 is only an asymptote if you extend the graph for negative values of t.


I know that. I was just curious as to why the textbook even added it in.
Reply 5
Original post by Inevitable
I know that. I was just curious as to why the textbook even added it in.


Just ignore it!

Either the textbook author thought he was being "helpful", or maybe the intention was to stimulate a discussion between a student and class teacher, or some other random thing!

For the real, physical situation being modelled here, t >= 0 , so the "asymptote" is utterly irrelevant :smile:

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