Graphing Exponential Growth & Decay

Graphing Exponential Growth & Decay

Y- a×b x-h +K

A- Multiplier

A>1- Stretch

A<a<1- Compression

A<0 (negative)- Flipped over x-axis

B- Base has an exponential (always positive)

0>b<1- Decay (always decreasing)

Asymptote-y=k

Domain-(-∞, ∞) =all real numbers

Range-y>k (a=positive)

          y<k (a=negative)

Exponential equations domain is always all real numbers.

General Forms of a Sequence

General Forms of a Sequence

 

Sequence- Is an ordered list of terms or elements.

Arithmetic Sequence- the difference between one term and the next is a constant. Also called the Common Difference.

Geometric sequence formula-  In a Geometric Sequence each term is found by multiplying the previous term by a constant. Also called the Common Ratio.

Finite sequence- Is a function with domain 1,2,3.

Infinite sequence- Is a function with domain 1,2,3,4.... etc.

Series- Is the sum of a sequence.

Explicit formula- Each domain is an answer not based on any values.

Recursive Formula- Each domain is a answer based on a previous answer.

Compound Interest Formula

Compound Interest Formula

P= principal amount (the initial amount you borrow or deposit)

r= annual rate of interest (as a decimal)

n= number of years the amount is deposited or borrowed for

A= amount of money accumulated after n years, including interest

n= number of times the interest is compounded per year

Example: An amount of $1,500.00 is deposited in a bank paying an annual interest rate of 4.3%, compounded quarterly. What is the balance after 6 years?

Solution: Using the compound interest formula, we have that

P = 1500, r = 4.3/100 = 0.043, n = 4, t = 6.

So,the balance after 6 years is approximately $1,938.84.