Answer:
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.
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)