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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 =

Respuesta :

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Answer:

C= 82.1116

k=-0.0007192

Step-by-step explanation:

[tex]p=Ce^{kx}\\40=Ce^{k1000}\\30=Ce^{k1400}\\[/tex]

Applying logarithmic properties yields in the following linear system:

[tex]ln(40) = ln(C) + 1000k\\ln(30) = ln(C) + 1400k[/tex]

Solving for k:

[tex]ln(40) = ln(C) + 1000k\\ln(30) = ln(C) + 1400k\\400 k = ln(30)-ln(40)\\k=-0.0007192[/tex]

Solving for C:

[tex]40=Ce^{-0.0007192*1000}\\C= \frac{40}{e^{-0.0007192*1000}}\\C=82.1116[/tex]

C= 82.1116

k=-0.0007192

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