Unit 2 pre calc 4a (4.1-4.6)

Question 1

How do you know if a function is increasing and called an exponential growth

Answer 1

when a >0 and b>1
ex. f(x) = 2^x

Question 2

How do you know if a function is decreasing and called an exponential decay

Answer 2

when a >0 and 0<b<1
ex. f(x) = (1/2) ^x

Question 3

What is always the same for Exponential growth and decay?

Answer 3

D: all real numbers
R: y>o
Y intercept: (0,1)
asymptote: y=0

Question 4

Transformation rules:
a. f(x+h)
b. f(x-h)
c. f(x) + k
d. f(x) -k
e-f(x)
f. f(-x)

Answer 4

a. shifts left
b. shifts right
c. shifts up
d. shifts down
e. reflects over the x axis
f. reflects over the y axis

Question 5

What is the exponential growth and decay function equation? And what do all of the variables mean?

Answer 5

growth: f(t) = a(1+r)^t
decay: f(t) = a(1-r)^t
a is the initial amount, r is the growth or decay rate (as a decimal) and t is the length of time

Question 6

What is the continuous growth and decay function? And what do all the variables mean?

Answer 6

A=Pe^rt
r is positive in growth and negative in decay
P is initial amount
e is e
r is rate of change and t is time

Question 7

What is the compound interest equation? and what do all the variables mean?

Answer 7

A=P(1+(r/n))^(nt)
A is the final/total amount
P is the starting amount
r is the rate as a decimal
n is the number of times compounded per year
t is the time in years

Question 8

For compound interest what are the different numbers n can be?
a. weekly
b. biannual/semiannually
c. bimonthly
d. monthly
e. quarterly
f. daily

Answer 8

a. 52
b. 2
c. 24
d. 12
e. 4
f. 365

Question 9

What is the equation for continuously compounded interest?

Answer 9

A=Pe^rt

Question 10

what is logarithmic form and exponential form

Answer 10

Logarithmic form: log(subscript b) a = x
Exponential form: b^x =a

Question 11

Change of base formula

Answer 11

Ina/inb or loga/logb

Question 12

What is natural logarithm

Answer 12

log (subscript e) x -> In x
ex. In x = 4 goes to e^4 = x

Question 13

Basic properties of Logarithms
a. log(subscript b) 1 = ?
b log (subscript b) b =?

Answer 13

a. 0
b. 1

Question 14

Logarithm product property

Answer 14

log (subscript b) (m times n) -> log (subscript b) m+ log (subscript b) n
ex. log (subscript 3) 8 + log (subscript 3) 3x = log (subscript 3) 24x

Question 15

Logarithm Quotient property

Answer 15

Log (subscript b) m/n -> log ( subscript b) m - log ( subscript b) n
ex -> log 80 - log 16 = log 5

Question 16

Logarithm Power property

Answer 16

log ( subscript b) (m^n) -> n log ( subscript b) m

Question 17

for problems like f(x) = 3^x what are the things we know?
b>1

Answer 17

D: all real numbers
R: y>0
y intercept: (0, 1)
Asymptote: y =0
increasing interval: (-infinity, infinity)
decreasing interval: none
End behavior: as x -> infinity, f(x) -> infinity
as x -> - infinity, f(x) -> 0

Question 18

For problems like f(x) = 1/2 ^x what are the things we know?
0<b<1

Answer 18

D: all real numbers
R: y>0
Y int: (0,1)
Asymptote: y=0
Inc interval: none
Dec interval: (-infinity, infinity)
End behavior: as x -> infinity, f(x) -> 0
as x -> - infinity, f(x) -> infinity

Question 19

For problems like f(x) = log (subscript 3) x what are the things we know?
b > 1

Answer 19

D: x>o
R: all real numbers
x int: (1,0)
Asymptote: x = 0
Inc interval: 0, infinity
Dec interval: none
End behavior: as x -> infinity, f(x) -> infinity
as x -> 0, f(x) -> -infinity

Question 20

For problems like f(x)= log (subscript 1/2) x what are the things we know?
0<b<1

Answer 20

D: x>0
R: all real numbers
x int: (1, 0)
Asymptote: x = 0
Inc interval: none
Dec interval 0, infinity
End behavior: as x -> infinity, f(x) -> -infinity
as x -> 0, f(x) -> infinity