Question

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)

Answer 1

(a) 1610 units

(b) 915 units

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