1. 8.8 Logistic Growth Functions

2. Objectives/Assignment
Evaluate and graph logistic growth functions
Use logistic growth functions
Assignment: odd

3. General form Logistic Growth Functions
a, c, r are positive real constants
y =

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

5. Graph on your calculator:

6. Graph on your calculator:

7. Graph on your calculator:

8. 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.

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

10. 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 it’s 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

11. Graph Asy: y=0, y=6 Y-int: 6/(1+2)=6/3=2 Max growth: (ln2/.5 , 6/2) =
(1.4 , 3)
(0,2)

12. Your turn! Graph:
Asy: y=0 & y=3
Y-int: (0,1/2)
Max growth: (.8, 1.5)

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

14. Your turn!
Solve:
.46 ≈ x