Padlet: Unit 5 Vocabulary CCM1 by emma

Common Ratio

emma8 — 2014-01-22 21:26:16 UTC

Thanks to...

emma8 — 2014-01-22 21:27:57 UTC

Sources:

http://www.mathplanet.com/education/pre-algebra/learning-more-about-the-four-rules-of-arithmetic/geometric-sequences-of-numbers

http://www.mathsisfun.com/algebra/sequences-sums-geometric.html

http://www.digitalc3.com/?p=651

http://www.mathwords.com/e/explicit_formula.htm

http://en.wikipedia.org/wiki/Exponential_function

http://www.mathwarehouse.com/exponential-decay/images/

Example + Picture

emma8 — 2014-01-22 21:29:19 UTC

Real world application

emma8 — 2014-01-22 21:29:34 UTC

You might use common ratio to examine how much something grew, or increased.

For example, if you were charting time (days) versus growth (inches) of a bean plant, you might put the

range into a sequence and examine the common ratio.

COMMON CORE 1 VOCABULARY UNIT 5

emma8 — 2014-01-22 21:32:21 UTC

A Padlet by Emma

Initial Term

emma8 — 2014-01-22 21:34:09 UTC

emma8 — 2014-01-22 21:35:14 UTC

The very first term in a sequence.

emma8 — 2014-01-22 21:38:03 UTC

In a sequence: the ratio of a term to the previous. Is represented by "r"

Example + Picture

emma8 — 2014-01-22 21:42:42 UTC

Real world application

emma8 — 2014-01-22 21:43:09 UTC

The initial term is like the y intercept:

it tells you what the starting cost, (length, height, etc.) was.

NOW-NEXT

emma8 — 2014-01-22 21:45:44 UTC

emma8 — 2014-01-22 21:46:10 UTC

A form causing one number to get to the next number in a sequence.

Expressed with the terms NOW and NEXT, a function (+. -. *. /), and a number that is with the function.

Example

emma8 — 2014-01-23 21:15:11 UTC

2, 1, 0, -1, -2

NOW-2= NEXT

Start: 2

Picture

emma8 — 2014-01-23 21:28:19 UTC

by Emma Grindstaff using Paint software

Real World Application

emma8 — 2014-01-23 21:29:38 UTC

Whenever something or

someone goes through linear

changes over time, it can be

represented by NOW-NEXT. One

case of this might be rainfall on

a given day of steady showers.

Geometric Sequence

emma8 — 2014-01-24 00:35:01 UTC

emma8 — 2014-01-24 00:35:21 UTC

A sequence in which the same number is multiplied/divided by the same element to get the next element.

Picture

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Example

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2, 4, 8, 16, 32, 64

Each time, the term is multiplied by 2. Therefore it is a gemectric sequence.

Exponental Growth

emma8 — 2014-01-24 00:41:26 UTC

emma8 — 2014-01-24 00:41:48 UTC

when the exponent has a value greater than one, so the number is growing.

Example + Picture

emma8 — 2014-01-24 00:44:09 UTC

Real world application

emma8 — 2014-01-24 00:44:51 UTC

An example of this could be population growth in a country where population is controlled, like China. If each family is allowed to have 1 child, and each child has 1 child, and each child has 1 child, then that would be exponential growth.

Real world application

emma8 — 2014-01-24 00:45:21 UTC

Money situations can apply to geometric sequences, such as percentages.

Explicit Form

emma8 — 2014-01-24 00:54:58 UTC

emma8 — 2014-01-24 00:55:22 UTC

A geometric function written in the form form A(n) = a * rn - 1, where a is the initial value, r is the common ratio, and n is the term number

Picture + Example

emma8 — 2014-01-24 00:57:19 UTC

Real World Application

emma8 — 2014-01-24 00:58:55 UTC

Explicit form is just another way to write a normal, everyday geometric function. Geometric functions can be found in lots of places in our world!

Exponential Function

emma8 — 2014-01-24 01:04:24 UTC

emma8 — 2014-01-24 01:04:46 UTC

is used to model a relationship in which a constant change in the independent variable gives the same proportional change (percent of increase or decrease) in the dependent variable.

Example + Picture

emma8 — 2014-01-24 01:05:52 UTC

The natural exponential function y = e^x

Real world Application

emma8 — 2014-01-24 01:06:37 UTC

A variety of things could be represented in exponential function, such as population of people or animals.

Exponential Decay

emma8 — 2014-01-24 01:08:45 UTC

emma8 — 2014-01-24 01:09:17 UTC

when the exponent has a number less than 0.

emma8 — 2014-01-24 01:10:14 UTC

Example + Picture

emma8 — 2014-01-24 01:10:15 UTC

Real world application

emma8 — 2014-01-24 01:10:46 UTC

Some bacteria's death is exponential diecay.