Logistic Functions S-Curve Model

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

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

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

Example 1 – Telephones in Households 100 50 20 40 60

Example 1 – Telephones in Households 100 50 20 40 60

Example 1 – Telephones in Households 100 50 20 40 60

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

Example 1 – Telephones in Households

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

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

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

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

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