Exponential and Logarithmic Functions

User Generated

znlnq42

Mathematics

Description

  1. OPEN ENDED Give an example of a value of b for which y = bx represents exponential decay.
  2. Writing in Math Use the information about Women’s basketball on page 498 to explain how an exponential function can be used to describe the teams in a tournament. Include an explanation of how you could use the equation y = 2xto determine the number of rounds of tournament play for 128 teams and an example of an inappropriate number of teams for a tournament.
  3. Writing in Math Use the information about sound on page 529 to explain how a logarithmic scale can be used to measure sound. Include the relative intensities of a pin drop, a whisper, normal conversation, kitchen noise, and a jet engine written in scientific notation. Also include a plot of each of these relative intensities on the scale below and an explanation as to why the logarithmic scale might be preferred over the scale below.

Unformatted Attachment Preview

Exponential Functions GET READY for the Lesson 2016 NCA ste The NCAA women's basketball tournament 2006 NCAA Women's Tournament begins with 64 teams UNC Duke and consists of 6 rounds of play. The MIDEAST - UNC Duke EAST winners of the first round play against Tennessee Maryland U Conn each other in the second round. The Maryland winners then move Utah LSU from the Sweet Duke Sixteen to the Elite WEST -- Maryland LSU MIDWEST Eight to the Final Four and finally to the Maryland Stanford Championship Game. The number of teams y that compete in a tournament of x rounds is y = 24. Exponential Functions in an exponential function like y = 2*, the base is a constant, and the exponent is a variable. Let's examine the graph of y = 2* EXAMPLE Graph an Exponential Function Sketch the graph of y= 2*. Then state the function's domain and range. Make a table of values. Connect the points to sketch a smooth curve. x y = 2 8 y = 2 -3 2-3 = 1 7 12v7 -2 2-2 = 1/2 6 5 1 2-1 = 1 0 20 = 1 Notice that the domain of y = 2 includes irrational numbers 1/2 27 = √2 As the value of x decreases, 3
Purchase answer to see full attachment
User generated content is uploaded by users for the purposes of learning and should be used following Studypool's honor code & terms of service.

Explanation & Answer

Here are the answers, please tell me if you have any problem.

1. Example of a value of b for which y = bx represents exponential decay:
For exponential decay b should be positive integer less than 1 such as:
1

1

1- 𝑏 = , 𝑦 = ( )𝑥
2
1

2- 𝑏 = , 𝑦 =
3

2
1
( )𝑥
3

2. Exponential function can be used to describe the teams in a tournament:
From Page 518, it is shown that if we have 1 round then the number of
teams is 21=2, if we have 2 rounds then the number of teams is 22=4, if we
have 3 rounds then the number of teams is 23=8, and so on as at each
round every team only plays against one other team, so every round the
number of teams is reduced by its half value, so we use exponential
function in the form of 𝑦 = 2𝑥 where y is the number of teams, x is the
number of rounds to describe the teams in a tournament.
To determine the number of rounds of tournament play for 128 teams:
By applying the previous equation where y= 128 then128 = 2𝑥
∴ 𝑥 = 7 𝑟𝑜𝑢𝑛𝑑𝑠
Example of an inappropriate number of teams for a tournament:
- If number of rounds is 7 then an inappropriate number of teams is 100,
120, 90, as 27 = 128 ≠ 100 ≠ 120 ≠ 90
- If number of rounds is 6 then an inappropriate number of teams is 80,
70, 60, as 26 = 64 ≠ 80 ≠ 70 ≠ 60
3. To explain how a logarithmic scale can be used to measure sound:
As the sound intensity has enormous range of possible values, we use the
logarithmic scale to measure it by writing the values as powers of ten and
track their exponents.
The relative intensities of:
- A pin drop= 100
- A whisper= 102
- Normal conversation= 106
- Kitchen noise= 1010
- A jet engine= 1012

A jet engine

A pin drop
A whisper
Normal conversation
Kitchen noise

A plot of each...


Anonymous
Really great stuff, couldn't ask for more.

Studypool
4.7
Trustpilot
4.5
Sitejabber
4.4

Related Tags