Formulas For Ch 4 and logistic functions

Question 1

Continuously compounded

Answer 1

A = Pe^rt

Question 2

Half life

Answer 2

A = P (1/2)^t/h

Question 3

Compounded interest

Answer 3

A = P(1+ r/n)^nt

N: how many times a year it’s compounded

Question 4

Doubling time

Answer 4

A = P (2)^t/d

Question 5

Decay constant

Answer 5

N(t) = N e^-kt

0

Question 6

Other equation

Answer 6

A= Pe^kt
K= rate of growth

Question 7

Decibel (sound)

Answer 7

D=10log(I/IT)

D-> decibel level
I-> intensity of sound measured in watts/ sq. meters
IT-> 1 x 10^-12 W/ m^2

Question 8

Richter scale

Answer 8

M = 2/3 log(E/Eo)
M= magnitude
E: seismic energy released by earthquake

Eo: energy released by reference earthquake; 10^4.4J

Question 9

Logistic functions

Answer 9

C C
————– ————-
1 + a • b^x 1+ a• e ^-kx

Question 10

C in logistic function

Answer 10

Limit to growth

Question 11

A in logistic functions

Answer 11

Initial amount

Question 12

K in logistic function

Answer 12

Rate

Question 13

Horizontal asymptotes of logistic functions

Answer 13

Y= 0 y= c

Question 14

Domain and range of logistic functions

Answer 14

D: all real
Range: (0, c)