Log in to add a comment

Log in to add a comment

The Brainliest Answer!

Certified answers contain reliable, trustworthy information vouched for by a hand-picked team of experts. Brainly has millions of high quality answers, all of them carefully moderated by our most trusted community members, but certified answers are the finest of the finest.

price = p

demand = x

we need to write demand as a function of price. So f(p) = x.

1.

p = 42 - 0.4x ; 0 ≤ x ≤ 105

for x = 0, p = 42

for x = 105, p = 42 - 0.4×105 = 42 - 42 = 0

p = 42 - 0.4x

⇒ p - 42 = -0.4x

⇒ x = -(p-42)/0.4

⇒ x = 105 - 2.5p

⇒**f(p) = 105 - 2.5p ; 0 ≤
p ≤ 105.**

2.

p = 125 - 0.02x ; 0 ≤ x ≤ 6250

for x = 0, p = 125

for x = 6250, p = 125 - 0.02×6250 = 125 - 125 = 0

p =125 - 0.02x

⇒ p - 125 = -0.02x

⇒ -x = (p - 125)/0.02

⇒ -x = 50p - 6250

⇒ x = 6250 - 50p

⇒**f(p) = 6250 - 50p ; 0 ≤ p ≤ 125.**

3.

p = 50 - 0.5x² ; 0 ≤ x ≤10

for x = 0, p = 50

for x = 10, p = 50 - 0.5×10² = 50 - 50 = 0

p =50 - 0.5x²

⇒ p - 50 = -0.5x²

⇒ 0.5x² = 50 - p

⇒ x² = (50 - p)/0.5 = 100 - 2p

⇒ x = √(100 - 2p)

⇒**f(p) = √(100 - 2p); 0 ≤ p ≤ 50.**

4.

p = 180 - 0.8x² ; 0 ≤ x ≤15

for x = 0, p = 180

for x = 15, p = 180 - 0.8×15² = 180-180 = 0

p =180 - 0.8x²

⇒ p - 180 = -0.8x²

⇒ 0.8x² = 180 - p

⇒ x² = (180 - p)/0.8 = 225 - 1.25p

⇒ x = √( 225 - 1.25p)

⇒**f(p) = √(** **225 - 1.25p); 0 ≤ p ≤ 180.**

5.

p = 25e^{-x/20} ; 0≤x≤20

for x = 0, p = 25

for x = 20, p = 25e^{-20/20} = 25/e

p = 25e^{-x/20}

⇒ p = 25/e^{x/20}

⇒ e^{x/20} = 25/p

⇒ log( e^{x/20} ) = log (25/p)

⇒ x/20 = log (25/p)

⇒ x = 20 log (25/p)

⇒**f(p) = 20 log (25/p);
0 ≤ p ≤ 25/e**
** **

6.

p = 45 - e^{x/4} ; 0≤x≤12

for x = 0, p = 45-1 = 44

for x = 12, p = 45 - e^{12/4} = 45- e³

p = 45 - e^{x/4}

⇒ p - 15= e^{x/4}

⇒ e^{x/4} = 45 - p

⇒ log( e^{x/4} ) = log (45 - p)

⇒ x/4 = log (45 - p)

⇒ x = 4 log (45 - p)

⇒**f(p) = 20 log (25/p); 45-e**³** ≤ p ≤ 44**

7.

p =80 - 10 ln x; 1 ≤ x ≤ 30

for x = 1, p = 80 - 0 = 80

for x = 30, p = 80 - 10 ln (30) = 10 (8 - ln 30)

p = 80 - 10 ln x

⇒ p - 80 = - 10 ln x

⇒ 10 ln x = 80-p

⇒ ln x = (80-p)/10 = 8 - 0.1p

⇒ x = e^{8 - 0.1p}

⇒**f(p) = e^{8 - 0.1p}; 10(8- ln 30) ≤ p ≤ 80**
** **

8.

p =ln(500 - 5x); 0 ≤ x ≤ 90

for x = 0, p =ln 500

for x = 90, p = ln(500 - 5×90) = ln 50

p = ln(500 - 5x)

⇒ ln(500 - 5x) = p

⇒ 500 - 5x = e^p

⇒ -5x = e^p - 500

⇒ x = (e^p - 500)/(-5) = 100 - 0.2e^p

⇒**f(p) = 100 - 0.2e^p; ln 50 ≤ p ≤ ln 500**

demand = x

we need to write demand as a function of price. So f(p) = x.

1.

p = 42 - 0.4x ; 0 ≤ x ≤ 105

for x = 0, p = 42

for x = 105, p = 42 - 0.4×105 = 42 - 42 = 0

p = 42 - 0.4x

⇒ p - 42 = -0.4x

⇒ x = -(p-42)/0.4

⇒ x = 105 - 2.5p

⇒

2.

p = 125 - 0.02x ; 0 ≤ x ≤ 6250

for x = 0, p = 125

for x = 6250, p = 125 - 0.02×6250 = 125 - 125 = 0

p =125 - 0.02x

⇒ p - 125 = -0.02x

⇒ -x = (p - 125)/0.02

⇒ -x = 50p - 6250

⇒ x = 6250 - 50p

⇒

3.

p = 50 - 0.5x² ; 0 ≤ x ≤10

for x = 0, p = 50

for x = 10, p = 50 - 0.5×10² = 50 - 50 = 0

p =50 - 0.5x²

⇒ p - 50 = -0.5x²

⇒ 0.5x² = 50 - p

⇒ x² = (50 - p)/0.5 = 100 - 2p

⇒ x = √(100 - 2p)

⇒

4.

p = 180 - 0.8x² ; 0 ≤ x ≤15

for x = 0, p = 180

for x = 15, p = 180 - 0.8×15² = 180-180 = 0

p =180 - 0.8x²

⇒ p - 180 = -0.8x²

⇒ 0.8x² = 180 - p

⇒ x² = (180 - p)/0.8 = 225 - 1.25p

⇒ x = √( 225 - 1.25p)

⇒

5.

p = 25e^{-x/20} ; 0≤x≤20

for x = 0, p = 25

for x = 20, p = 25e^{-20/20} = 25/e

p = 25e^{-x/20}

⇒ p = 25/e^{x/20}

⇒ e^{x/20} = 25/p

⇒ log( e^{x/20} ) = log (25/p)

⇒ x/20 = log (25/p)

⇒ x = 20 log (25/p)

⇒

6.

p = 45 - e^{x/4} ; 0≤x≤12

for x = 0, p = 45-1 = 44

for x = 12, p = 45 - e^{12/4} = 45- e³

p = 45 - e^{x/4}

⇒ p - 15= e^{x/4}

⇒ e^{x/4} = 45 - p

⇒ log( e^{x/4} ) = log (45 - p)

⇒ x/4 = log (45 - p)

⇒ x = 4 log (45 - p)

⇒

7.

p =80 - 10 ln x; 1 ≤ x ≤ 30

for x = 1, p = 80 - 0 = 80

for x = 30, p = 80 - 10 ln (30) = 10 (8 - ln 30)

p = 80 - 10 ln x

⇒ p - 80 = - 10 ln x

⇒ 10 ln x = 80-p

⇒ ln x = (80-p)/10 = 8 - 0.1p

⇒ x = e^{8 - 0.1p}

⇒

8.

p =ln(500 - 5x); 0 ≤ x ≤ 90

for x = 0, p =ln 500

for x = 90, p = ln(500 - 5×90) = ln 50

p = ln(500 - 5x)

⇒ ln(500 - 5x) = p

⇒ 500 - 5x = e^p

⇒ -5x = e^p - 500

⇒ x = (e^p - 500)/(-5) = 100 - 0.2e^p

⇒