the demand equation for a certain clock radio is given by p=400-.06e^0.003x. find the demand,x, for the price of p=99

Question

The equation for this problem is p=400-0.06e^0.003x . 

Answer 1

p = 400 - 0.06e^0.003x

 

99 = 400 - 0.06e^0.003x

 

-301 = -0.06e^0.003x

 

5016.67 = e^0.003x

 

 

e ≈ 2.72

 

5016.67 = 2.72^0.003x

 

 

Since the x value we want to find is an exponent, we must log both sides and bring the exponent as the coefficient of the log.

 

 

log(5016.67) = 0.003x log(2.72)

 

x = [log(5016.67] / [0.003 log(2.72)]

 

x = 2838.38

 

 

The demand is 2838.38 clocks.