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Fudgin [204]
3 years ago
15

Devante has a lunch account in the school cafeteria His starting balance at the beginning of the month is $35.50. The first wook

, Davante bought 3 lunches and his account balance was $28.00. The second week. Devante
bought 5 lunches and his account balance was 515 50

In a model that relates the balance of his lunch account as a function of the number of lunches he buys, what does the rate of change represent?


A: the number of lunches he purchases


B: the starting balance of his lunch account


C: the amount of money in his lunch account


D: the amount of money he pays for each lunch
Mathematics
1 answer:
Alisiya [41]3 years ago
7 0

Answer:

D the amount of money he pays for each lunch

Step-by-step explanation:

In each lunch Devante has, he pays 2,50 $ according to:

Money in t = t₀     he has  35,50 $      paid 3 lunches and spent

35,50 - 28  =  7,5

Then the cost of each lunch is    7,5 / 3   =  2,5 $

After that

bought    5 lunches and spent   28  - 15,5  = 12,50

Again    12,5 / 5   =  2,5 $

Now the model for the situation is a straight line with a slope 2,5

In an  x , y cartesian system in which  y is money in the account  and x is the number of lunches, such a straight line will be

y  =  b  -  m*x      ( b the intercept on y  and  m the negative slope)

y  =  35,50 - 2,5*x

So  answering the question is lyrics  D  the amount of money he pays for each lunch

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<h2>Exponential Functions</h2>

Exponential functions are typically organized in this format:

f(x) = a*c^x

To find the equation given the graph of an exponential function:

  1. Identify the horizontal asymptote
    ⇒ <em>asymptote</em> - a line towards which a graph appears to travel but never meets
    ⇒ If the horizontal asymptote is not equal to 0, we add this at the end of the function equation.
  2. Identify the y-intercept
    ⇒ This is our <em>a</em> value.
  3. Identify a point on the graph and solve for <em>c</em>

<em />

<h2>Solving the Question</h2>

Identify the horizontal asymptote

In this question, it appears to be x = 0.

Identify the y-intercept

The y-intercept is the value of <em>y</em> at which the graph appears to cross the y-axis. In this graph, it appears to be 100. This is our <em>a</em> value. Plug this into f(x) = a*c^x:

f(x) = 100*c^x

Solve for <em>c</em>

We can use any point that falls on the graph for this step. For instance, (1,50) appears to be a valid point. Plug this into our equation and solve for <em>c</em>:

f(x) = 100*c^x\\50 = 100*c^1\\50 = 100*c\\\\c=\dfrac{1}{2}

Plug <em>c</em> back into our original equation:

f(x) = 100*(\dfrac{1}{2})^x

<h2>Answer</h2>

f(x) = 100*(\dfrac{1}{2})^x

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<em>The table that shows the relative frequency of data is in the below further explanation.</em>

\texttt{ }

<h3>Further explanation</h3>

A set is a clearly defined collection of objects.

To declare a set can be done in various ways such as:

  • With words or the nature of membership
  • With set notation
  • By registering its members
  • With Venn diagrams

\texttt{ }

Multiplying set A x B is by pairing each member of set A with each member of set B.

<u>Example:</u>

<em>A = {1, 2, 3}</em>

<em>B = {a, b}</em>

Then

A x B = {(1, a), (1, b), (2, a), (2, b), (3, a), (3, b)}

\texttt{ }

Union of set A and B ( A ∪ B ) is rewriting each member A and combined with each member B.

Intersection of set A and B ( A ∩ B ) is to find the members that are both in Set A and Set B.

<u>Example:</u>

<em>A = {1, 2, 3, 4}</em>

<em>B = {3, 4, 5}</em>

A ∪ B = {1, 2, 3, 4, 5}

A ∩ B = {3, 4}

Let us now tackle the problem!

\texttt{ }

<em>A sports club has 84 members who learned baseball, and 42 of those members also learned basketball.</em>

\left[\begin{array}{ccc}&Play Baseball&Don't Play Baseball\\Play Basketball&\boxed{42}& \\Don't Play Basketball& & \end{array}\right]

\texttt{ }

Number of members who learned baseball but did not learn basketball will be ( 84 - 42 ) = 42 members

\left[\begin{array}{ccc}&Play Baseball&Don't Play Baseball\\Play Basketball&42& \\Don't Play Basketball&\boxed{42}& \end{array}\right]

\texttt{ }

<em>There are 25 students who did not learn baseball but learned basketball</em>

\left[\begin{array}{ccc}&Play Baseball&Don't Play Baseball\\Play Basketball&42&\boxed{25} \\Don't Play Basketball&42& \end{array}\right]

\texttt{ }

<em>8 students did not learn either baseball or basketball</em>

\left[\begin{array}{ccc}&Play Baseball&Don't Play Baseball\\Play Basketball&42&25 \\Don't Play Basketball&42&\boxed{8} \end{array}\right]

\texttt{ }

<em>Total Number of Students = 42 + 42 + 25 + 8 = 117</em>

\texttt{ }

Table of relative frequency

\left[\begin{array}{ccc}&Play Baseball&Don't Play Baseball\\Play Basketball&\boxed{\frac{42}{117}}&\boxed{\frac{25}{117}} \\Don't Play Basketball&\boxed{\frac{42}{117}}&\boxed{\frac{8}{117}} \end{array}\right]

\texttt{ }

<h3>Learn more</h3>
  • Mean , Median and Mode : brainly.com/question/2689808
  • Centers and Variability : brainly.com/question/3792854
  • Subsets of Set : brainly.com/question/2000547

<h3>Answer details</h3>

Grade: High School

Subject: Mathematics

Chapter: Sets

Keywords: Sets , Venn , Diagram , Intersection , Union , Mean , Median , Mode

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