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# The graph of the equation y=22.2-42.2*0.6^x has a horizontal asymptote. What would be the equation of this asymptote?

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The graph of the equation y=22.2-42.2*0.6^x has a horizontal asymptote. What would be the equation of this asymptote?

Feb 20, 2020

#1
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y = 22.2  - 42.2* 0.6^x

Note  that  as  x  gets  larger and larger, the term 42.2*0.6^x    virtually  evaluates  to 0

So.....the  horizontal asymptote  =  y  = 22.2 - (0)  ⇒  y = 22.2

See the graph of this here :   https://www.desmos.com/calculator/luywbdkzfx   Feb 20, 2020
#2
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Thank you! In my assignment they also ask me what the horizontal assympote ""means/shows"". The assignment is about counting the owls in a city, and x originally was t for time. So if t gets larger the quantity of owls practically turns to zero then?

Guest Feb 20, 2020
#3
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No..... it means that as  t gets larger and larger,  the owl population will stabilize at 22.2  [  this must  be in some unit like thousands  ]   CPhill  Feb 20, 2020
#4
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Ah I see thanks! I made a teeny tinsy mistake in the equation (it's supposed ot be 220.2 instead of 22.2). Does it still mean the same then?

Guest Feb 21, 2020