exam 3

Question 1

what is the growth rate of an exponential function

Answer 1

b^x

Question 2

what are the two main types of bases?

Answer 2

growth: b>1
decay: 0<b<1

Question 3

what is c in f(t)=cb^t

Answer 3

the y intercept and starting value

Question 4

determine b, c and r for g(x)=20(0.3)^x

Answer 4

b=0.3
c=20
r=1-.3=0.7

Question 5

what is the function for a numeric experiment

Answer 5

(1+(1/n))^n

Question 6

what is the number e

Answer 6

~2.7

Question 7

what are the two forms of logarithms

Answer 7

LOGbX=y or b^y=x

Question 8

what are the 3 log properties (where A,B>0)

Answer 8

1. LOGb(AB)=LOGbA+LOGbB
2. LOGb(A/B)= LOGbA-LOGbB
3. LOGbA^n=LOGbA*n

Question 9

how do logs and exponentials compare

Answer 9

for any base b where x is defined, LOGb(b^x)=x and b^LOGbX=x; since y=LOGbX, b^x reverses the roles of x and y in y=b^x

Question 10

what is the domain of ln(x)

Answer 10

(0,infinity)

Question 11

what are the 3 steps to solving an exponential/log function

Answer 11

1. determine that any and all powers are the same
2. do algebra first
3. use logs or expos

Question 12

how to solve log equations

Answer 12

1. use exponentials
2. use log properites and algebra

Question 13

what is a sinusoidal function?

Answer 13

a sin or cos transformation

Question 14

what is the function for a sinusoidal

Answer 14

Asin(Bx+C)+D
(can also be cos)

Question 15

what does A, B, C, and D represent in Asin(Bx+C)+D?
how do you find it?

Answer 15

A- amplitude or range, the vertical stretch: |A|
B- the period or repetition point: 2π/B
C- the horizontal shift: C/B
D- vertical shift/midline

Question 16

what are the key points for sin or cos (ie: x=?)

Answer 16

0, π/2, π, 3π/2, 2π

Question 17

how do you find the key points of a sinusiodal function?

Answer 17

(2π/B)/4

Question 18

what is the function to find a horizontal shift

Answer 18

k*(period/4)+HS