The annual number of units demanded, x x , of a product (in thousands) by consumers at unit price p , in dollars per unit, is modeled by the formula p2+x=14,

Question

a. Write x explicitly as a function of p

(b) What is the practical domain of the function?

(c) How many units will be sold at a unit price of $0.7?

(d) At what price(s) is/are 2137 units sold?

Answer 1

x= 14-p^2 is the demand curve or demand function

x(p) = 14-p^2, x explicitly as a function of price p

p<sqr14

p<about $3.74 = max price before no one buys anything or everyone buys zero. price>$3.74 prices everyone out of the market

0 < p < 3.74

or in interval notation (0,3.74)

at $0.70 = 70 cents price, x =14-.7^2 = 14-.49 = 13.51 thousand

= 13,510 units sold

2137 sold means 2.137 thousand =14-p^2

p^2 = 14-2.137= 11.863

p = sqr11.863= 3.44

price = $3.44 per unit sold when 2137 are sold