Revenue

Repeat Exercise 45 given that when p = $5, x = 300 units, and when p = $4, x = 400 units.

i. C = 9.76, k = - 0.00223

ii. the demand model can be written as;

p = 9.76e^ (-0.00223x)

Question:

i. Find th values of C and k.

ii. Write the demand.

Step-by-step explanation:

The provided demand model is p = Ce^ (kx) the values of p and x are;

p = $5, x = 300 units and when p = $4, x=400 units.

We need to find the values of C and k

First case; Substituting the first case p = $5, x = 300

5 = Ce^300k ... 1

Second case: substituting p = $4, x = 400

4 = Ce^400k ... 2

Dividing eqn1 by 2

5/4 = (Ce^300k) / (Ce^400k)

5/4 = e^ (300k-400k)

5/4 = e^ (-100k)

-100k = ln (5/4)

k = ln (5/4) / (-100)

k = - 0.00223

At substituting k into eqn1

5 = Ce^ (300 * - 0.00223)

C = 5/e^ (300 * - 0.00223)

C = 9.76

Therefore the demand model can be written as;

p = 9.76e^ (-0.00223x)