The demand function for a product is given by

p = 10,000 [1 − (5/5 + e^−0.001x)]

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
p = $1000
and
p = $1500.
(Round your answers to the nearest integer.)

(a) p = $1000 _____units
(b) p = $1500 _____units

2 answers

Just plug in p and solve for x:

1000 = 10000(1 - 5/(5+e^-.001x))
.1 = 1 - 5/(5+e^-.001x)
.9 = 5/(5+e^-.001x)
5+e^-.001x = 5/.9
e^-.001x = .5555
-.001x = ln .5555
.001x = .58778
x = 587.78
NAE NAE