1. Logistic Functions
S-Curve Model

2. Characteristics
Growth (or decay) begins slowly, then increases rapidly and levels off.
Describes a type of growth seen in:
Population growth in a specific location
Growth of seedlings
Bacteria growth in a petri dish
Infectious disease growth
Information (rumors) spread rate

3. Logistic Functions: Graph
c: upper limit (horizontal asymptote)
y(0): y-intercept

4. Logistic Functions: Equation
b>0 (growth) or b<0 (decay)
y=c – horizontal asymptote
e - natural logarithm (Euler’s Number)

5. Example 1 – Telephones in Households
100 50 20 40 60

6. Example 1 – Telephones in Households
100 50 20 40 60

7. Example 1 – Telephones in Households
100 50 20 40 60

8. Example 1 – Telephones in Households
TI-84 only!
STAT – 1:Edit…
Enter L1, L2
STAT – CALC: B:Logistic
Enter, Enter

9. Example 1 – Telephones in Households

10. Example 1 – Telephones in Households
According to this model, what is the number of telephones in households today?
x = 2018 – 1935 = 83
y = 95.43

11. Example 2 – Infant Mortality Rate (U.S.)

12. Example 2 – Infant Mortality Rate (U.S.)

13. Example 2 – Infant Mortality Rate (U.S.)

14. According to this model, what is the infant mortality rate today?
Example 2 – Infant Mortality Rate (U.S.)
According to this model, what is the infant mortality rate today?
x = 2018 – 1950 = 68
y = 2.6