Study

Question 1

The function f(x) = a^x with a > 0 and a ≠ 1 is

Answer 1

The exponential function with base a

Question 2

The exponential function with base a

Answer 2

f(x) = a^x with a > 0 and a ≠ 1

Question 3

What is x^2 and what is 2^x

Answer 3

Power function and exponential function

Question 4

Power function and exponential function

Answer 4

x^2 and 2^x

Question 5

Domain and range of exponential functions

Answer 5

(-∞, ∞) and (0, ∞)

Question 6

(-∞, ∞) and (0, ∞)

Answer 6

Domain and range of exponential functions

Question 7

How do you graph y=a^x?

Answer 7

Y intercept at 0,1

Point at (1,a)

Lim a^x = ∞
x —> ∞

Lim a^x = 0
x —> -∞

Question 8

How do you graph the opposite of y = a^x?

Answer 8

Y intercept (0,1)

Point at (1,a)

Point at (-1, 1/a)

Lim a^x = 0
x—> ∞

Lim a^x = ∞
x—> -∞

Question 9

Y intercept at 0,1

Point at (1,a)

Lim a^x = ∞
x —> ∞

Lim a^x = 0
x —> -∞

Answer 9

y = a^x

Question 10

Y intercept (0,1)

Point at (1,a)

Point at (-1, 1/a)

Lim a^x = 0
x—> ∞

Lim a^x = ∞
x—> -∞

Answer 10

Opposite of y=a^x

Question 11

What shift is this?

y=a^x-c

Answer 11

Shift right c units

Question 12

How do you shift right c units in an exponential function?

Answer 12

y=a^x-c

Question 13

Reflections in exponential functions

Answer 13

y=-a^x (x-axis)

y=a^-x (y-axis)

Question 14

What is this transformation?

y=Ca^x

Answer 14

Stretch if C>1

Shrink if 0

Question 15

Examples of exponential growth / decay

Answer 15

Capital, population, radioactive isotopes

Question 16

Capital, population, radioactive isotopes

Answer 16

Examples of exponential growth / decay

Question 17

Discrete compound interest formula

Answer 17

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

Question 18

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

Answer 18

Discrete compound interest formula

Question 19

What is r and n in discrete compound interest formula?

Answer 19

N is number of times compounded like (annually, semi-annually, quarterly, monthly, or daily) and r is perfentage

Question 20

Continuously compounded interest formula

Answer 20

A=Pe^rt

Lim (1+1/h)^h = e

Question 21

A=Pe^rt

Lim (1+1/h)^h = e

Answer 21

Continuously compounded interest formula

Question 22

Exponential growth and decay formula

Answer 22

A(t)=A(o)e^kt or A(o)(e^k)^t

Initial amount is A(o)

K is relative time rate of graph (k > 0) for growth and (k < 0) for decay

Question 23

A(t)=A(o)e^kt or A(o)(e^k)^t

Initial amount is A(o)

K is relative time rate of graph (k > 0) for growth and (k < 0) for decay

Answer 23

Exponential growth and decay formula

Question 24

How do you graph:

y=logaX

Answer 24

X intercept (1,0)

Domain: (0, ∞)

Range: (-∞, ∞)

Question 25

X intercept (1,0) Domain: (0, ∞) Range: (-∞, ∞)

Answer 25

y=logaX

Question 26

The logarithm with base a is defined by

Answer 26

y=logaX iff x=a^y

Question 27

y=logaX iff x=a^y

Answer 27

Logarithm with base a

Question 28

Convert to logarithmic form: 4^3=64 (1/2)^4=1/16 a^-2=7

Answer 28

3=log4(64) 4=log1/2(1/16) -2=loga(7)

Question 29

3=log4(64) 4=log1/2(1/16) -2=loga(7

Answer 29

4^3=64 (1/2)^4=1/16 a^-2=7

Question 30

Convert to exponential form: log3(243)=5 log2(5)=x loga(N)=x

Answer 30

243=3^5 5=2^x N=a^x

Question 31

243=3^5 5=2^x N=a^x

Answer 31

log3(243)=5 log2(5)=x loga(N)=x

Question 32

The number loga(x) is

Answer 32

The power that we raise a to in order to get x

Question 33

The power that we raise a to in order to get x

Answer 33

loga(x)

Question 34

log5(25) log2(16) log1/3(9) log7(7) log16(1) log4(1/2)

Answer 34

log5(5^2)=2 log2(2^4)=4 log1/3(3^2)=log1/3^-2 log7(7)=1 log16(1)=0 log4(1/2)=-1/2

Question 35

log5(5^2)=2 log2(2^4)=4 log1/3(3^2)=log1/3^-2 log7(7)=1 log16(1)=0 log4(1/2)=-1/2

Answer 35

log5(25) log2(16) log1/3(9) log7(7) log16(1) log4(1/2)

Question 36

How is log1/3(9) evaluated?

Answer 36

1. ) log1/3(3^2) is written 2. ) log1/3((1/3)^-1)^2 is written since 3 = 1/3^-1 3. ) answer is log1/3(1/3^-2)

Question 37

Basic properties of logarithms

Answer 37

loga(a)=1 loga(1)=0 loga(a^x)=x for any real x a^loga(x)= x for any x > 0

Question 38

loga(a)=1 loga(1)=0 loga(a^x)=x for any real x a^loga(x)= x for any x > 0

Answer 38

Basic properties of logarithms

Question 39

How do you find the domain of a logarithmic function?

Answer 39

The numbers inside the parenthesis must be set to 0

Question 40

What is the domain of: g(x) = logz(x+1/x-3)

Answer 40

(-∞,-1) U (3, ∞) since the numerator and denominator have to be positive

Question 41

What is “the exponential function”

Answer 41

e^x

Question 42

e^x

Answer 42

“The exponential function”

Question 43

Common logarithm and natural logarithm difference

Answer 43

Common is log base 10 “logx” Natural is log base e “lnx”

Question 44

Evaluate: lne^4

Answer 44

4

Question 45

Logarithm rules loga(xy) loga(x/y) loga(x^y)

Answer 45

loga(x) + loga(y) logaX - loga(y) y • loga(x)

Question 46

loga(x) + loga(y) logaX - loga(y) y • loga(x)

Answer 46

loga(xy) loga(x/y) loga(x^y)

Question 47

Exponent rules a^x • a^y ax/ay (a^x)^y

Answer 47

a^x+y a^x-y a^xy

Question 48

a^x+y a^x-y a^xy

Answer 48

a^x • a^y ax/ay (a^x)^

Question 49

Change if base formula

Answer 49

loga(x) = ln(x)/ln(a)

Question 50

loga(x) = ln(x)/ln(a)

Answer 50

Change of base formula

Question 51

Radioactive decay formula

Answer 51

h=-ln2/k

Question 52

h=-ln2/k

Answer 52

Radioactive decay formula