Question 1200876
**1. Demand Curve (Exponential)**

* **Function:** 
   * Qd = a * e^(-bP) 
      * Where:
         * Qd is the quantity demanded
         * P is the price
         * a and b are positive constants

* **Characteristics:**
    * **Negative Slope:** As price (P) increases, the exponent (-bP) becomes more negative. This leads to a decrease in the value of e^(-bP) and consequently a decrease in quantity demanded (Qd). This reflects the law of demand.
    * **Asymptotic to Price Axis:** As price approaches infinity, the exponent (-bP) approaches negative infinity. This causes e^(-bP) to approach zero, meaning the quantity demanded approaches zero but never reaches it. 
    * **Smooth and Continuous:** The exponential function provides a smooth and continuous curve, which is generally observed in real-world demand relationships.

**2. Supply Curve (Logarithmic)**

* **Function:**
   * Qs = c * ln(d + P)
      * Where:
         * Qs is the quantity supplied
         * P is the price
         * c and d are positive constants

* **Characteristics:**
    * **Positive Slope:** As price (P) increases, the argument of the natural logarithm (d + P) also increases. This leads to an increase in the value of ln(d + P) and consequently an increase in quantity supplied (Qs). This reflects the law of supply.
    * **Asymptotic to Price Axis (potentially):** The exact behavior depends on the value of 'd'. If 'd' is zero, the supply curve will have a vertical asymptote at P = 0. If 'd' is positive, the curve will approach a vertical line as price approaches negative infinity (though this region might not be economically relevant).
    * **Smooth and Continuous:** The logarithmic function provides a smooth and continuous curve, which is generally observed in real-world supply relationships.

**Note:**

* These are simplified models. Real-world demand and supply curves can be more complex and influenced by various factors beyond just price.
* The specific values of the constants (a, b, c, d) will determine the exact shape and position of the curves.

I hope this helps! Let me know if you'd like to explore any of these concepts in more detail.