The demand function for a product is given by p=3000e^-q/3, where p is price per unit when q units are demanded.
a. at what price per unit will the quantity demanded equal 6 units?
b. If the price is $159.40 per unit, how many units will be demanded? (nearest whole unit)
a. p = 3000e^-6/3 = 3000e^-2 = $406 per unit
b. 159.40 = 3000e^-q/3
e^-q/3 = 159.4/3000
ln(e^-q/3) = ln(159.4/3000)
-q/3 = ln(159.4/3000)
q = -3ln(159.4/3000) = 8.8 = 9 units
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