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# 1. What are the asymptotes of the graph of f(x)?

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1. What are the asymptotes of the graph of f(x)?

y = 3

y = 0

y = 20

y = 9

2. What is the point of maximum growth rate for the logistic function f(x)? Round to the nearest hundredth.

(0.42, 3)

(0.85, 12)

(0.85, 24)

(0, 4)

jbouyer  Feb 24, 2018

#1
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1.

$$y=\frac{20}{1+9e^{3x}} \\~\\ y(1 + 9e^{3x})=20 \\~\\ 1 + 9e^{3x}=\frac{20}{y} \\~\\ 9e^{3x}=\frac{20}{y}-1 \\~\\ 9e^{3x}=\frac{20-y}{y} \\~\\ e^{3x}=\frac{20-y}{9y} \\~\\ 3x=\ln(\frac{20-y}{9y}) \\~\\ x=\frac{\ln(\frac{20-y}{9y})}{3}$$

There is an asymptote when   9y  =  0   which is when   y = 0

There is an asymptote when   $$\frac{20-y}{9y}$$  =  0   which is when   y = 20

Here's a graph: https://www.desmos.com/calculator/9czjghjp9s

hectictar  Feb 24, 2018
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#1
+6536
+1

1.

$$y=\frac{20}{1+9e^{3x}} \\~\\ y(1 + 9e^{3x})=20 \\~\\ 1 + 9e^{3x}=\frac{20}{y} \\~\\ 9e^{3x}=\frac{20}{y}-1 \\~\\ 9e^{3x}=\frac{20-y}{y} \\~\\ e^{3x}=\frac{20-y}{9y} \\~\\ 3x=\ln(\frac{20-y}{9y}) \\~\\ x=\frac{\ln(\frac{20-y}{9y})}{3}$$

There is an asymptote when   9y  =  0   which is when   y = 0

There is an asymptote when   $$\frac{20-y}{9y}$$  =  0   which is when   y = 20

Here's a graph: https://www.desmos.com/calculator/9czjghjp9s

hectictar  Feb 24, 2018

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