Math Problem Statement

From the table provided, determine the demand function based on price and demand, then plot the demand curve.

Solution

The table provided lists "Harga" (Price) and "Permintaan" (Demand). The goal is to determine the demand function based on this data and plot the demand curve.

Step 1: Analyze the data

The data points are:

  • (Harga, Permintaan)
    • (20, 20)
    • (18, 36)
    • (16, 32)
    • (14, 38)

Step 2: Determine the demand function

The demand function is typically linear, in the form:

Qd=aP+bQ_d = aP + b

Where:

  • QdQ_d is the quantity demanded (Permintaan).
  • PP is the price (Harga).
  • aa is the slope of the demand curve.
  • bb is the intercept.

To find aa and bb, we can use two points from the table and solve the system of equations.

Let's solve this now.The demand function based on the given data is:

Qd=8P+180Q_d = -8P + 180

Where:

  • QdQ_d is the quantity demanded (Permintaan),
  • PP is the price (Harga).

Step 3: Plot the demand curve

Now, we can create a graph to visualize this demand curve. I'll plot it for you.It seems like I can’t do more advanced data analysis right now. Please try again later.

However, the demand function we derived is:

Qd=8P+180Q_d = -8P + 180

You can plot this function by using the price values in the range of your data (for example, from 10 to 25) and the corresponding demand values using the formula.

If you have any more questions or would like further details, feel free to ask!

Related Questions:

  1. How would changes in the slope affect the demand curve?
  2. How can we estimate demand elasticity using this demand function?
  3. What would the demand be at a price of 12?
  4. How can external factors affect the intercept bb in the demand function?
  5. Can the demand curve ever have a positive slope? Why or why not?

Tip: Always check if your data points fit a linear model or if a different type of function might describe the relationship better.

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Math Problem Analysis

Mathematical Concepts

Linear Functions
Algebra

Formulas

Q_d = aP + b (Demand function formula)

Theorems

Slope-intercept form

Suitable Grade Level

Grades 9-12