1) The amount of digital information created each month globally, t months after
ID: 2877272 • Letter: 1
Question
1) The amount of digital information created each month globally, t months after the begginning of 2008, is approximately f(t)=400(t/2+1)1.09 (0<= t <= 36 ) billion gigabytes.
a) How many billion gigabytes of information were created at the beginning of 2008?
b) Haw fast was digital information being created at the beginning of 2010(t=24)?
2) The mangment of Acrosonic plans to market the Electrostat, an electrostatic speaker system. The marketing department has determined that the demand function for these speakers is P= -0.04x + 800 (0<= x <= 20,000) where P denotes the speaker's unit price ( in dollars) and x denotes the quantity function R.
A) Find the revenue function R .
B) Find the marginal revenue function R' .
C) Find the exact revenue for selling the 5,001st speaker system.
D) Find the approximate revenue for selling the 5,001 st speaker system
Explanation / Answer
1 a . Given f (t) = 400 [ t/2 +1] 1.09 starting from 2008
put t= 0 we get the no of information created in 2008
f(0) = 400 ( 1.09) = 436 billion gigabytes
b . in 2010 ( after 3 years , 24 months , put t = 24 )
f( 24) = 400( 12+1) 1.09 = 400x13x1.09=5668 billion gigabytes
2 . demand fn = P (x) = - 0.04 x +800
a . Revenue fn = R (x) = x P(x) = - 0.04 x2 +800x
b . Marginal Rev fn = R ' = - 0.08 x +800
c in P(x) put x = 5001 , P(x) = - 0.04 x5001 +800= 600
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