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Elan Coil [88]
3 years ago
5

A small business assumes that the demand function for one of its new products can be modeled by p = Cekx. When p = $40, x = 1000

units, and when p = $30, x = 1400 units. (a) Solve for C and k. (Round C to four decimal places and k to seven decimal places.) C = k =
Mathematics
1 answer:
Maru [420]3 years ago
6 0

Answer:

C= 82.1116

k=-0.0007192

Step-by-step explanation:

p=Ce^{kx}\\40=Ce^{k1000}\\30=Ce^{k1400}\\

Applying logarithmic properties yields in the following linear system:

ln(40) = ln(C) + 1000k\\ln(30) = ln(C) + 1400k

Solving for k:

ln(40) = ln(C) + 1000k\\ln(30) = ln(C) + 1400k\\400 k = ln(30)-ln(40)\\k=-0.0007192

Solving for C:

40=Ce^{-0.0007192*1000}\\C= \frac{40}{e^{-0.0007192*1000}}\\C=82.1116

C= 82.1116

k=-0.0007192

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