https://file.aiquickdraw.com/mathbot/file/1728853585864njtiz2ka.jpg

Let's analyze the problem step by step.

### Given:
The demand function for oil is \( D(p) = \frac{900}{p} \), where \( p \) is the price per barrel in dollars. 

We are asked to find:
1. The demand when \( p = 35 \).
2. The decrease in demand when \( p \) increases to 36.
3. The increase in demand when \( p \) decreases to 34.

### 1. **Demand at \( p = 35 \):**
We already know the answer here:
\[
D(35) = 25.71 \, \text{barrels}
\]
This value is directly given in the image.

### 2. **Decrease in demand when \( p \) rises to 36:**
We can calculate the demand at \( p = 36 \) using the same demand function \( D(p) \).

\[
D(36) = \frac{900}{36}
\]

Simplifying this:

\[
D(36) = 25 \, \text{barrels}
\]

Now, the decrease in demand from \( p = 35 \) to \( p = 36 \) is:

\[
\text{Decrease} = D(35) - D(36) = 25.71 - 25 = 0.71 \, \text{barrels}
\]

### 3. **Increase in demand when \( p \) decreases to 34:**
Similarly, we calculate the demand at \( p = 34 \).

\[
D(34) = \frac{900}{34}
\]

Using a calculator:

\[
D(34) \approx 26.47 \, \text{barrels}
\]

Now, the increase in demand from \( p = 35 \) to \( p = 34 \) is:

\[
\text{Increase} = D(34) - D(35) = 26.47 - 25.71 = 0.76 \, \text{barrels}
\]

### Final results:
- The **decrease** in demand when \( p \) rises to 36 is **0.71 barrels**.
- The **increase** in demand when \( p \) decreases to 34 is **0.76 barrels**.

Would you like further explanation or have any specific questions about the process?

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Here are 5 related questions for deeper understanding:
1. What would happen to the demand if the price increases to 40 dollars?
2. How does the demand change if the price drops to 30 dollars?
3. How can we calculate the percentage change in demand for a small price change?
4. What is the significance of the inverse relationship between price and demand?
5. How would the demand behave if the price approaches infinity?

**Tip:** When calculating demand or supply, always ensure to check for non-linear relationships between price and quantity.

The demand for a commodity generally decreases as the price is raised. Suppose that the demand for oil (per capita per year) is D(p) = 900/p barrels, where p is the price per barrel in dollars. Find the demand when p = 35. Estimate the decrease in demand if p rises to 36 and the increase in demand if p is decreased to 34.

Solve a demand function problem where D(p) = 900/p barrels. Learn how to find the demand at p = 35, calculate the decrease in demand when p rises to 36, and the increase when p drops to 34. This problem illustrates the inverse relationship between price and quantity demanded, suitable for high school students studying economics or algebra.

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