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?

Guest Feb 20, 2020

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4⁺⁰ Answers

+128474

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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

CPhill Feb 20, 2020

+1

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

+128474

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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

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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

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