Exponential and logarithmic functions

Domain for all exponentials:

(-infinity, infinity)

(ab)^x =

(a^x)(b^x)

a^x * b^x =

(ab)^x

What is (1/2)^x equal to?

2^-x or a exponential graph with a reflection over Y

What is (1/2)^-x

2^x or a regular exponential graph

Compound Interest Formula

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

Formula for continuously compounded interest

A=Pe^rt (PERT formula)

Exponential Growth/Decay

A=p(1+-r)^t

Exponential Growth

A=p(1+r)^t

What are you finding when you use the geometric sequence equation?

An, or the specific term in a geometric sequence

What is the difference between growth rate and growth factor?

Growth rate is how much something grows per time unit, so if r is 12% then the growth rate is 12%. The growth factor factors in (hehe) the fact that in order for it to be growth, r must be >1. If the growth rate is 12%, the growth factor is 1.12 or 112%. The growth rate is what is multiplied every time in the equation.

What do all exponentials have?

Horizontal asymptote

The population, A, of a certain bacteria can be modeled by A=50e^1.2t where t is the time in hours. What is the initial population? What is the growth factor? What is the percent increase (rate of growth?)

Initial bacteria is 50. Growth FACTOR is e^1.2 because this is what you are CONTINUALLY multiplying by. The rate of growth is 20%.

If a word problem regarding compounding interest asks how long it will take for a certain amount of money to accumulate, what is the most likely course of actions?

Plug into Y= in calculator (putting this in here because this is something I would forget to do on the quiz)

If a Petri dish has bacteria that double every half hour, what is the rate of growth every half hour? What is the growth factor every half hour? What is the hourly rate of growth? What is the hourly growth factor?

Rate of growth every half hour is 100% as it gains 100% of what it originally had. The growth factor every half hour is 200%. The hourly rate of growth is 300% because it gains 300% of what it originally had. The hourly growth factor is 400%.

infinite geometric series

Sn=A1/1-r

Geometric Series

Sn=a1(1-r^n)/1-r

What must you ALWAYS include when writing a recursive formula?

THE FIRST TERM

What is the main difference between recursive and explicit formulas?

The recursive formula relies on the previous term in the sequence to find the next one, explicit does not.

What are you finding when you use the geometric series equation?

The sum of all the terms in a sequence up to the specified term

How will you know if a table displays exponential behavior?

The terms must have a common ratio, where An/An-1 is a constant. It will NOT have a constant SLOPE.

What is the difference between geometric sequence vs exponential growth/decay?

This is a tough one. The geometric sequence equation looks like An=a1(r^n-1) and growth/decay looks like A=p(1+-r)^t. Generally, growth/decay will deal with time while a sequence will deal with rounds of something where there is no time in-between.

when is the ONLY TIME you can use infinite geometric series?

When r<1 because it will always approach zero

Can the geometric series equation be used with sequences where r>1?

Yes. The geometric series is used to find the sum of all terms UP TO the NTH term (which will be given to you in the problem). The INFINITE geometric series equation can only be used in sequences where r<1.

a^x * a^y =

a^x+y

Geometric Sequence

an=a1(r)^n-1

(b^n)^m=

b^n*m