Logistic Growth Functions Hello my name is Super

General form Logistic Growth Functions • a, c, b are positive real constants •

Evaluating • f(x) = • f(-3) = ≈. 0275 • f(0) = = 100/10

• From these graphs you can see that a logistic growth function has

Decreasing growth rate Increasing growth rate Point of maximum Growth where the graph Switches

The graphs of • The horizontal lines y=0 & y=c are asymptotes • The

Graph • • Asy: y=0, y=6 Y-int: 6/(1+2)=6/3=2 Max growth: (ln 2/. 5 ,

Your turn! Graph: • Asy: y=0 & y=3 • Y-int: (0, 1/2) • Max

Solving Logistic Growth Functions • Solve: • • • 50 = 40(1+10 e-3 x)

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Logistic Growth Functions Hello, my name is Super Power Hero.

General form Logistic Growth Functions • a, c, b are positive real constants • y=

Evaluating • f(x) = • f(-3) = ≈. 0275 • f(0) = = 100/10 = 10

Graph on your calculator:

• From these graphs you can see that a logistic growth function has an upper bound of y=c. • Logistic growth functions are used to model real-life quantities whose growth levels off because the rate of growth changes – from an increasing growth rate to a decreasing growth rate.

Decreasing growth rate Increasing growth rate Point of maximum Growth where the graph Switches from growth To decrease.

The graphs of • The horizontal lines y=0 & y=c are asymptotes • The y intercept is (0, ) • The Domain is all reals and the Range is 0<y<c • The graph is increasing from left to right • To the left of its point of maximum growth, the rate of increase is increasing. • To the right of it’s point of maximum growth, the rate of increase is decreasing

Graph • • Asy: y=0, y=6 Y-int: 6/(1+2)=6/3=2 Max growth: (ln 2/. 5 , 6/2) = (1. 4 , 3) (0, 2)

Your turn! Graph: • Asy: y=0 & y=3 • Y-int: (0, 1/2) • Max growth: (. 8, 1. 5)

Solving Logistic Growth Functions • Solve: • • • 50 = 40(1+10 e-3 x) 50 = 40 + 400 e-3 x 10 = 400 e-3 x. 025 = e-3 x ln. 025 = -3 x 1. 23 ≈ x

Your turn! • Solve: • . 46 ≈ x