Chapter 3 Exponential, Logistic, and
Logarithmic Functions
3­1 Exponential and Logistic Functions
Exponential: f(x) = a bx a is non­zero b > 0 and ≠1
(x in the exponent)
a: initial value
b: base (rate)
Jan 23­7:31 AM
Which of the following are exponential functions?
y = x7
y = 63
Jan 23­7:38 AM
1
Determine an exponential function for the values given.
initial
X
Y
­2
6
­1
3
0
3/2
1
3/4
2
3/8
*anything to 0 power = 1
*plug in a point for x and y to solve for b
Jan 23­7:41 AM
Exponential Growth: a > 0, b > 1
Exponential Decay: a > 0, b < 1
*horizontal asymptote
Jan 23­7:56 AM
2
The Natural Base: e
*named for Leonhard Euler
e ≈ 2.72
Exponential Function and Base e
f(x) = a ekx
growth: a > 0, k > 0
decay: a > 0, k < 0
Jan 23­8:58 AM
Using the data and assuming the growth is exponential, when would the population of Austin surpass 800,000?
Year
Population
1990
465,622
2000
656,562
Jan 23­9:17 AM
3
Logistic Growth Function
growth "levels out"; predator/prey, population
f(x) = c
1 + a bx
OR
f(x) = c
1 + a e­kx
c is the limit to growth
a, b, c, k > 0, b < 1
c
Jan 23­9:07 AM
The population of Ohio can be modeled by the given function where P is the population in millions, and t is the number of years since 1900. Based on this function, when was the population of Ohio 10 million?
P(t) = 12.79
1 + 2.402e ­.0309t
Jan 23­9:23 AM
4
pg.286 #2­12 even, 32­38 even
42, 44, 52­58 even
Jan 23­9:27 AM
5

スライド 1

B.Tech. (Dec, 2014)

H. Timm Elektronik GmbH + Humboldtstr. 29 + D

Data Booklet

Download File

Download (386Kb)

数式処理実習 [第7回]

スライド 1