help ? A clothing store chain found that t days after the end of a sales promoti

Question

help ?

A clothing store chain found that t days after the end of a sales promotion the volume of sales was given by S (t) = 20000(l + e-0.5t) In dollars. Find the rate of change of the sales volume when t = 1, t = 2, t = 3, and t = 4. The monthly demand for a certain brand of perfume is given by P = 100e-0.0002x + 150 where p denotes the retail unit price in dollars and x denotes the quantity (in 1 ounce bottles) demanded. Find the rate of change of the price per bottle when x = 1000, x = 2000. What is the price per bottle when x = 1000, x = 2000.

Explanation / Answer

S = 2000(1 + e^-0.5 t)

dS/dt = - 2000*0.5 (e^(-0.5t)) = -1000(e^(-0.5t))

at ,

t =1 ,

dS/dt = -606.53

at t=2

dS/dt = -367.88

at t= 3,

dS/dt = -223.13

at t=4,

dS/dt = -135.335

2]

p= 100 e^(-0.0002x+150)

dp/dx= (-0.0002)*100 * e^(-0.0002x+150)

dp/dx = 0.02 * e^(-0.0002x+1.50)

at x = 1000,

p = 1.141*10^67

dp/dx = 2.282*10^63

at

x= 2000

p = 9.3423*10^66

dp/dx = 1.868*10^63

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