what is the horizontal and vertical asymptote of P(m)=(90(1+1.5m))\(1+0.5m)

Since the denominator cannot be zero we set

1+0.5m = 0

0.5m = -1

m = -1/0.5 = -2

Therefore there is a vertical asymptote at m = -2

To find the horizontal asymptote set the limit as m approaches infinity

90(1+1.5m) / 1+0.5m = 90+135m /1+0.5m

as m approaches infinity, the 90 in the numerator and the 1 in the denominator become insignificant, so

then we have 135m/0.5m = 270

So, the horizontal asymptote is at P = 270

Thank you for helping me with this problem, I could not figure out how to find the horizontal asymptote, only the vertical which I got right!

Yes. The horizontal asymptote is always the limit of the function as the domain approaches infinity.

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