Independent/dependent variable and modeling equations

In summary, Homework Statement 8. Amelia’s Marina rents rowboats for $12/hour. A cleaning fee of $20 is charged, when the boat is returned.a. Identify the independent and dependent variables, including units, for this scenario.The independent variable is the $20 cleaning fee. The dependent variable is $12 per hour. If I wrote this as the formula as a line it would be written as: Y = 12x + 20.20 would be the initial value and initial value is always the independent variable. While 12 would be the slope, and the slope is always the dependent variable.b. Write an equation that models this scenario.a equation
  • #1
Kirito123
124
14

Homework Statement


8. Amelia’s Marina rents rowboats for $12/hour. A cleaning fee of $20 is charged, when the boat is returned.

a. Identify the independent and dependent variables, including units, for this scenario.b. Write an equation that models this scenario.

c. A nearby marina offers a higher hourly rate and lower cleaning fee. Suggest a realistic equation that could model that scenario.

Homework Equations


y = mx + b

3. The Attempt at a Solution

a. Identify the independent and dependent variables, including units, for this scenario.

The Independent variable is the $20 cleaning fee. The dependent variable is $12 per hour. If I wrote this as the formula as a line it would be written as: Y = 12x + 20.
20 would be the initial value and initial value is always the independent variable. While 12 would be the slope, and the slope is always the dependent variable.

b. Write an equation that models this scenario.

a equation that can model this scenario is y = mx + b. Were y is the total cost, m the amount of money per hour ($12). X represents the number of hours and b is the cleaning fee. If we were to put this in equation form it would look like this: Y = 12x + 20c. A nearby marina offers a higher hourly rate and lower cleaning fee. Suggest a realistic equation that could model that scenario.

The marina could offer $14 per hour ($14/hour), which is a higher hourly rate compared to the first marina, and an $11 cleaning fee after the rowboat is returned, which can be considered a lower cleaning fee compared to the cleaning fee offered by the first marina.
So using the equation y = mx + b, where y is the total cost, m is the amount of dollars per hour, x is the total amount of hours, and b is the cleaning fee, we can formulate an equation: y = 14x + 11.Im pretty sure that my solutions are correct, I just want to be 100% sure.
 
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  • #2
Kirito123 said:

Homework Statement


8. Amelia’s Marina rents rowboats for $12/hour. A cleaning fee of $20 is charged, when the boat is returned.

a. Identify the independent and dependent variables, including units, for this scenario.b. Write an equation that models this scenario.

c. A nearby marina offers a higher hourly rate and lower cleaning fee. Suggest a realistic equation that could model that scenario.

Homework Equations


y = mx + b

3. The Attempt at a Solution

a. Identify the independent and dependent variables, including units, for this scenario.

The Independent variable is the $20 cleaning fee. The dependent variable is $12 per hour. If I wrote this as the formula as a line it would be written as: Y = 12x + 20.
20 would be the initial value and initial value is always the independent variable. While 12 would be the slope, and the slope is always the dependent variable.
Those are not variables at all. x and y are the variables.

Later on you say that x represents the number of hours a boat is rented and y is the total rental cost.
Which of those is the dependent variable, and which is the independent variable?
b. Write an equation that models this scenario.

a equation that can model this scenario is y = mx + b. Where y is the total cost, m the amount of money per hour ($12). X represents the number of hours and b is the cleaning fee. If we were to put this in equation form it would look like this: Y = 12x + 20c. A nearby marina offers a higher hourly rate and lower cleaning fee. Suggest a realistic equation that could model that scenario.

The marina could offer $14 per hour ($14/hour), which is a higher hourly rate compared to the first marina, and an $11 cleaning fee after the rowboat is returned, which can be considered a lower cleaning fee compared to the cleaning fee offered by the first marina.
So using the equation y = mx + b, where y is the total cost, m is the amount of dollars per hour, x is the total amount of hours, and b is the cleaning fee, we can formulate an equation: y = 14x + 11.Im pretty sure that my solutions are correct, I just want to be 100% sure.
 
  • #3
The independent in this case would be the hours and the dependent would be the total rental cost since the total rental cost depends on how long you rent the boat for. right?
 
  • #4
Kirito123 said:
The independent in this case would be the hours and the dependent would be the total rental cost since the total rental cost depends on how long you rent the boat for. right?
Right
 
  • #5
So i still don't understand were i went wrong?
 

Related to Independent/dependent variable and modeling equations

1. What is an independent variable?

An independent variable is a variable that is changed or controlled by the experimenter in a scientific experiment. It is also known as the "manipulated variable" as it is the variable that is manipulated to see how it affects the dependent variable.

2. How is an independent variable related to a modeling equation?

The independent variable is typically represented by the "x" in a modeling equation. It is the variable that is being manipulated or changed in order to see how it affects the dependent variable. The relationship between the independent and dependent variables is often represented by a graph or equation in order to analyze the data and make predictions.

3. What is a dependent variable?

A dependent variable is a variable that is observed or measured in a scientific experiment. It is also known as the "responding variable" as it is the variable that responds to changes in the independent variable. The value of the dependent variable is affected by the value of the independent variable.

4. How is a dependent variable represented in a modeling equation?

The dependent variable is typically represented by the "y" in a modeling equation. It is the variable that is being measured or observed and is affected by changes in the independent variable. The relationship between the independent and dependent variables is often represented by a graph or equation in order to analyze the data and make predictions.

5. What is the purpose of modeling equations in scientific experiments?

The purpose of modeling equations in scientific experiments is to represent the relationship between the independent and dependent variables. By using equations and graphs, scientists can analyze data, make predictions, and understand how changes in the independent variable affect the dependent variable. Modeling equations help to make the data and results of experiments more understandable and meaningful.

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