Math Problem Statement
Solution
The table in the image shows two variables: Harga (Price) and Permintaan (Demand). The goal is to determine the demand function from the data and plot the demand curve.
Table Data:
- Harga (Price) = 20, Permintaan (Demand) = 20
- Harga (Price) = 18, Permintaan (Demand) = 36
- Harga (Price) = 16, Permintaan (Demand) = 32
- Harga (Price) = 14, Permintaan (Demand) = 38
Step 1: Find the Demand Function
We can model the relationship between Harga (P) and Permintaan (Q) as a linear function: Where is the slope and is the intercept.
Let's calculate the slope using the formula: I'll calculate the slope between two points and the intercept to find the function.The demand function is:
Where:
- is the demand (Permintaan)
- is the price (Harga)
Step 2: Plot the Demand Curve
I will now plot the demand curve based on this equation.It seems like I can’t do more advanced data analysis right now. Please try again later.
However, you can manually plot the demand curve based on the function:
Here’s how:
- Set different values for (Price), like 14, 16, 18, and 20.
- Calculate (Demand) using the formula.
- Plot the points on a graph with Price on the x-axis and Demand on the y-axis.
Would you like any further clarifications or help with this?
Here are some related questions to deepen your understanding:
- How is the slope of the demand curve interpreted in economics?
- What does a negative slope imply about the relationship between price and demand?
- How would an increase in demand affect the function ?
- Can you explain what the intercept represents in this context?
- How would you modify the demand function if new data points were added?
Tip: When graphing a demand curve, always check if the relationship is linear or non-linear based on the data points.
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Math Problem Analysis
Mathematical Concepts
Linear Functions
Algebra
Demand Curve
Formulas
Q = aP + b (Linear Demand Function)
Slope formula a = (Q2 - Q1) / (P2 - P1)
Theorems
Linear Relationship Between Price and Demand
Suitable Grade Level
Grades 10-12