TEST 2

a^6/a^2

a^4 Rule: Subtract exponents when dividing

a3⋅a4

a3+4=a7
👉 Rule: Add exponents when multiplying

(a2)4

a2⋅4=a8
👉 Rule: Multiply exponents when raising a power

What are the 3 exponent rules?

• Multiply → ADD

• Divide → SUBTRACT

• Power → MULTIPLY

log(10000) = 4 log(10)

10000=104
So:

log⁡(10^4) = 4 log(10)

👉 Rule: log⁡(a^n)=nlog⁡(a)

When do you use logs?

When the variable is in the exponent

Compound interest formula?

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

What do the variables mean?

• P = starting money

• r = rate (decimal!)

• n = times per year

• t = years

What is the MOST COMMON mistake?

Not turning % into decimal
(5% = 0.05)

Continuous compounding formula?

A= Pe^rt

Simple interest formula?

A=P(1+rt)

How is simple interest different?

No exponent → NO compounding

What does log⁡(a^n) become?

n log(a)

What is log⁡(10)?

1 (base 10 logs)

How do you find doubling time?

Set A=2P then:

2= (1+ r/n)^nt

Solve for time t (doubling)?

t= log(2)

nlog(1+r/n)

Monthly compounding formula

A=P(1+r/12)^12t

Monthly deposit formula

A= PMT * (1+r/n)^nt-1/ r/n

When do you use annuity formula?

When money is deposited repeatedly (monthly, yearly)

Loan payment formula

PMT= P(r/n)

1-(1+r/n)^-nt

What is PMT?

Monthly payment

When do you use loan formula?

When paying off a loan (house, car, etc.)

Future value of annuity

A= PMT * (1+r)^t -1 / r

Solve for PMT

PMT= A*r / (1+r)^t - 1

Convert percent to decimal

Divide by 100
4.5% = 0.045

How to identify problem type?

• One deposit → compound formula

• Repeated deposits → annuity

• Loan → payment formula

First step in EVERY problem

Write formula BEFORE plugging numbers