(a) (f(x)) 1 = 2 (b) f 1 (x) = 2 (c) f(x 1 ) = 2 (a) Estimate and interpret D(5)
ID: 3090381 • Letter: #
Question
(a) (f(x))1 = 2 (b) f1(x) = 2 (c) f(x1) = 2 (a) Estimate and interpret D(5). (b) Find a formula for D(p) in terms of p. (c) Calculate and interpret D1(5). (d) Give an interpretation of the slope of D(p) in terms ofdemand. (e) Currently, the company can produce 400 units every week. Whatshould the price of the product be if the company wants to sell all400 units? (f) If the company produced 500 units per week instead of 400units per week, would its weekly revenues increase, and if so, byhow much? Let f(x) = ex. Solve each of thefollowing equations exactly for x. (a) (f(x))1 = 2 (b) f1(x) = 2 (c) f(x1) = 2 2) A company believes there is a linear relationshipbetween the consumer demand for its products and the price charged.When the price was $3 per unit, the quantity demanded was 500 unitsper week. When the unit price was raised to $4, the quantitydemanded dropped to 300 units per week. Let D(p) be the quantityper week demanded by consumers at a unit price of $p. (a) Estimate and interpret D(5). (b) Find a formula for D(p) in terms of p. (c) Calculate and interpret D1(5). (d) Give an interpretation of the slope of D(p) in terms ofdemand. (e) Currently, the company can produce 400 units every week. Whatshould the price of the product be if the company wants to sell all400 units? (f) If the company produced 500 units per week instead of 400units per week, would its weekly revenues increase, and if so, byhow much?Explanation / Answer
1.(a) (f(x))-1 = 2 (ex)-1 = 2 e-x = 2 1/ex = 2 ex = 1/2 ln(ex = ln(1/2) x = ln(1/2) 1.(b) y = ex ln(y) = ln(ex) x = ln(y) f-1(x) = ln(x) ln(x) = 2 x = e2 1.(c) f(x-1) = ex^-1 f(x-1) = e1/x e1/x = 2 ln(e1/x) = ln(2) 1/x = ln(2) x = ln(2)
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