Intro to Functions: The annual number of unites demanded, x, of a product (in thousands) by consumers at unit price p, in dollars per unit, is modeled by the formula

Question

The annual number of unites demanded, x, of a product (in thousands) by consumers at unit price p, in dollars per unit, is modeled by the formula

p2 + x = 14

a. Write x explicitly as a function of p:

x=

b. What is the practical domain of the function?

c. How many units will be sold at a unit price of $1.50?

d. At what price(s) is/are 2000 unites sold?

Answer 1

p^2 + x = 14

x= 14-p^2

domain is 0 < x < 14 (14,000)

x=14-(1.5)^2 = 14 - 2.25 = 11.75 = 11,750 units

p^2 = 14-2 = 12

p =sqr12 = 2sqr3 = about 2(1.732) = 3.464 = $3.46