+593 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)
+9466 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
+9466 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
