The price per unit when the demand equals 7000 units is $0, while the number of units demanded at a price $13.78 is 2000 units.
<h3>How do we use a demand function to calculate price and quantity?</h3>
The correct equation of the question is as follows:
p = 50(5^(−q/2)) ................................... (1)
Where p is the price per unit and q is a thousand units of the commodity.
a.) The price p per unit at which the demand will equal 7000 units can be calculated as follows:
Substituting q = 7000 into equation (1) we have:
p = 50(5^(−700/2))
p = 50 * 5^(-450)
p = 50 * 0
p = $0
b.) The number of units, to the nearest thousand units, that will be demanded if the price is $13.78 can be calculated as follows:
Substituting p = 13.78 into equation (1) and solving for q, we have:
13.78 = 50(5^(−q/2))
13.78 / 50 = 5^(−0.5q)
0.2756 = 5^(−0.5q)
Taking the log of both sides, we have:
log0.2756 = −0.5q * log5
−0.559720786764412 = −0.5q * 0.698970004336019
−0.5q = −0.559720786764412 / 0.698970004336019
−0.5q = −0.80077940869024
q = −0.80077940869024 / −0.5
q = 1.60155881738048
Since q is a thousand units, we have:
q = 1.60155881738048 * 1000 = 1601.55881738048
Rounding to the nearest thousand units, we have:
q = 2000
Learn more about the demand function here: brainly.com/question/28198225.
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