Demand The demand function for the product is given by

p = 5000 (1 - 4/4 + e^-0.002x)

where p is the price per unit (in dollars) and x is the number of units sold. Find the numbers of units sold for prices of (a) p = $200 and (b) p = $800.

p = 5000 (1 - 4/4 + e^-0.002x)

(a) 1610 units

(b) 915 units

Step-by-step explanation:

p = 5000 (1 - 4/4 + e^-0.002x)

(a) p = $200

200 = 5000 (1 - 1 + e^-0.002x)

200/5000 = e^-0.002x

e^-0.002x = 0.04

-0.002x = In 0.04 = - 3.22

x = - 3.22/-0.002 = 1610 units

(b) p = $800

800 = 5000 (1 - 4/4 + e^-0.002x)

800/5000 = e^-0.002x

e^-0.002x = 0.16

-0.002x = In 0.16 = - 1.83

x = - 1.83/-0.002 = 915 units