Answers

The Brainliest Answer!
2015-03-27T19:14:50+05:30

This Is a Certified 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-e³ ≤ 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
3 5 3
thanks a lot for answering
Awesome !!