Unit 2

Question 1

How are exponential functions defined?

Answer 1

F(x)= a^x where a> 0 and a Odense equal 1

Question 2

How do you solve exponential equations?

Answer 2

Make the base of both sides the same, then you can eliminate the bases and solve for the exponents

Question 3

What is the formula for simple interest?

Answer 3

I = Prt
I= simple interest
P= principle (amount borrowed or invested)
r= rate of interest per year
t= time in years

Question 4

What is the formula for compound interest?

Answer 4

A=P(1+r/m)^tm 
m= times per year
r= rate of interest per year
P= starting amount invested
t= number of years 
A= future amount

Question 5

What is the formula for finding the amount of interest you owe or paid?

Answer 5

Interest = A-P

Question 6

What is the formula for continuous compounding?

Answer 6

A=Pe^rt

Question 7

What is the equation converting exponential form to logarithmic form?

Answer 7

a^y=x -> loga(x)=y

Question 8

What does loga(a) equal?

Answer 8

1

A^1 = a

Question 9

What does loga(1) equal?

Answer 9

0

a^0=1

Question 10

What does loga(a^r) equal?

Answer 10

r

rloga(a) = r(1) = r

Question 11

How do you solve log equations with different a values in your calculator?

Answer 11

Loga(x)= log(x)/log(a)

Question 12

What is loga(x) equal to in ln?

Answer 12

Loga(x)=lnx/lna

Got any positive numbers where a does not equal 1

Question 13

What are the restrictions on a in loga(x)?

Answer 13

A>0

A cannot equal 1

Question 14

What is the formula for growth and decay problems? What does k mean?

Answer 14

y=y0e^kt
If k > 0, k is growth constant
If k<0, k is the decay constant

Y0- the amount or number of some quantity at t=0
K= rate of change

Question 15

For half life questions what do we make Y equal to in Y=Y0e^kt?

Answer 15

Y= 1/2 y0

Then cancel y0’s

Question 16

What is the conversion factor of degrees to radians?

Answer 16

180 degrees = Pie radians

Take degreees, divide by 180, multiply by pie

60/180 x pie = pie/3

Question 17

What’s is the cast rule?

Answer 17

Using quadrants we can determine which trigs are positive
SA
TC

Question 18

What is csc

Answer 18

1/sin

Question 19

What is sec?

Answer 19

1/cos

Question 20

What is cot?

Answer 20

1/tan

Question 21

What are the Pythagorean identities?

Answer 21

Sin^2+cos^2=1
Tan^2+1= sec^2
Cot^2+1 =csc^2

Question 22

What are the three sum identities?

Answer 22

Sin (A+B)= SinACosB+SinBCosA
Cos(A+B)= CosACosB-SinASinB
Tan(A+B)= TanA+TanB/ 1-TanATanB