Horizontal asymptote of exponential functions

Asked by maham237 @ 12/01/2021 in Mathematics viewed by 286 People

Find an exponential function with a horizontal asymptote y equals=2 whose graph contains the points (0,3) and (1,6).

Answered by maham237 @ 12/01/2021

$\bf y=a(b)^x\qquad \qquad (\stackrel{x}{0}~,~\stackrel{y}{3})\implies 3=a(b)^0\implies 3=a
\\\\\\
therefore\qquad y=3(b)^x\\\\
-------------------------------\\\\
(\stackrel{x}{1}~,~\stackrel{y}{6})\implies 6=3(b)^1\implies \cfrac{6}{3}=b^1\implies 2=b
\\\\\\
therefore\qquad y=3(2)^x$

now, exponential functions have a horizontal asymptote at the x-axis, namely when y = 0, however, if you just move this one with a vertical translation of 2, then the horizontal asymptote will be at 2 instead. y = 3(2)ˣ + 2

Which function has a horizontal asymptote of y 3

Asked by maham237 @ 25/04/2021 in Mathematics viewed by 300 persons

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Asked by maham237 @ 25/12/2020 in Mathematics viewed by 280 persons

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