Math Problem Statement

Dari tabel dibawah ini, Tentukan Fungsi Permintaan lalu buatlah Kurva Permintaan. (Given a table of price and demand values, determine the demand function and plot the demand curve.)

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: Q=aP+bQ = aP + b Where aa is the slope and bb is the intercept.

Let's calculate the slope aa using the formula: a=(Q2Q1)(P2P1)a = \frac{(Q_2 - Q_1)}{(P_2 - P_1)} I'll calculate the slope between two points and the intercept to find the function.The demand function is:

Q=8P+180Q = -8P + 180

Where:

  • QQ is the demand (Permintaan)
  • PP 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:

Q=8P+180Q = -8P + 180

Here’s how:

  1. Set different values for PP (Price), like 14, 16, 18, and 20.
  2. Calculate QQ (Demand) using the formula.
  3. 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:

  1. How is the slope of the demand curve interpreted in economics?
  2. What does a negative slope imply about the relationship between price and demand?
  3. How would an increase in demand affect the function Q=8P+180Q = -8P + 180?
  4. Can you explain what the intercept b=180b = 180 represents in this context?
  5. 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