Answered

Jordan has started a new dog-walking service. His total profits over the first 4 weeks are expressed in this table.

Time(weeks) Profits($)

1 150

2 300

3 450

4 600


Show that his business results can be described by a linear function. Graph this function and use the graph to predict his business profit 9 weeks after he opens. Explain why it is or is not a good idea to project his profits so far into the future. Give examples to support your answer.

Jordan has started a new dog-walking service. His total profits over the first 4 weeks are expressed in this table.Time(weeks) Profits($)1 1502 3003 4504 600Sho class=

Answer :

The linear function is a straight forward and predictable function;

The correct values and responses are;

a. The equation of the function is y = 150·x, which is linear

b. The profit after 9 weeks is predicted as $1,350

c. Why projecting so far into the future is not a good idea are;

  • Limited duration of business
  • Limited business capacity consideration
  • Limited number of dogs
  • Overspending, running out of cash

Reasons:

a. The business result can be described as a linear function because, the first difference between the y-values are equal

We have;

First difference = 600 - 450 = 450 - 300 = 300 - 150 = 150

Given that the first differences for both the y, and x-values are equal, the rate of change, which is the slope, is constant, and the equation of the graph can be written in the form, y = m·x + c, which is the equation of a straight line

The slope or rate of change of the  result is given as follows;

[tex]Slope, \, m =\dfrac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]

Therefore;

[tex]Slope, \, m =\dfrac{600-450}{4-3} = 150[/tex]

The equation of the graph of the result is therefore;

y - 600 = 150·(x -4)

∴ y = 150·x

b. Please find attached the required graph of the function created with MS Excel

When x = 9 weeks, we have;

The profit, y = 150 × 9 = 1,350

The profit after 9 weeks = $1,350

c. The reasons why it is not a good idea to project the profit far into the future are;

  • The domain and range of the graph are infinite while the dog walking business is finite
  • The number of dogs that can be serviced may become limited as the dog numbers increase
  • The number of dogs within the neighborhood may be limited while the projection is unlimited
  • The projection may lead to mismanagement of expenses, overspending which may lead to the business becoming short of funds

Learn more here:

https://brainly.com/question/23009258

https://brainly.com/question/14935763

${teks-lihat-gambar} oeerivona

Other Questions