The monthly demand for a certain brand of perfume is given by the demand equation p = 100e−0.0002x + 125 where p denotes the retail unit price (in dollars) and x denotes the quantity (in 1-oz bottles) demanded.

(a) find the rate of change of the price per bottle when x = 2000 and when x = 3000. (round your answers to four decimal places.)

x = 2000( ) dollars/bottle

x = 3000( ) dollars/bottle

(b) what is the price per bottle when x = 2000? when x = 3000? (round your answers to the nearest cent.)

x = 2000 $ ( )

x = 3000 $ ( )

a)

Rate of change of the price per bottle when x = 2000

p'(2000)= -0.0134

Rate of change of the price per bottle when x = 3000

p'(3000)= -0.011

b)

Price per bottle when x = 2000

$192

Price per bottle when x = 3000

$180

Step-by-step explanation:

The equation of the demand x in terms of the price p is

(a) Find the rate of change of the price per bottle when x = 2000 and when x = 3000. (Round your answers to four decimal places.)

These are p'(x) at x=2000 and x=3000

so

(b) What is the price per bottle when x = 2000? When x = 3000? (Round your answers to the nearest cent.)

These are p(2000) and p(3000)

linear pair postulates