Mobile-phone ad spending is expected to grow at the rate of R(t) = 0.8256t^0.04
ID: 2894161 • Letter: M
Question
Mobile-phone ad spending is expected to grow at the rate of R(t) = 0.8256t^0.04 (1 lessthanorequalto t lessthanorequalto 5) billion dollars/year between 2007 (t = 1) and 2011 (t = 5). The mobile-phone ad spending in 2007 was $0.9 billion. (a) Find an expression f(t) giving the mobile-phone ad spending in year t. f(t) (b) If the trend continued, what will be the mobile-phone ad spending in 2016? Annual sales (in millions of units) of a certain brand of netbook computers are expected to grow in accordance with the function f(t) = 0.18t^2 + 0.16t + 2.64 (0 lessthanorequalto t lessthanorequalto 4) per year, where t is measured in years, with t = 0 corresponding to 1997. How many netbook computers will be sold over the 4 year period between the beginning of 1997 and the end of 2000?Explanation / Answer
11)
f(t)=R(t) dt ,f(1)=0.9
f(t)=(0.8256t-0.04) dt
f(t)=(0.8256/(-0.04+1))t-0.04+1+c
f(t)=(0.8256/0.96)t0.96+c
f(t)=0.86t0.96+c
f(1)=0.9
=>0.86*10.96+c=0.9
=>0.86+c=0.9
=>c=0.9-0.86
=>c=0.04
f(t)=0.86t0.96+0.04
(b)
in 2016, t=10
ad amount spending in 2016 =f(10)
ad amount spending in 2016 =0.86*100.96+0.04
ad amount spending in 2016 =7.88 billion dollars
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12)
number of notebooks sold over 4 year period between 1997 and 2000 is =[0 to 4] [0.18t2+0.16t +2.64] dt
number of notebooks sold over 4 year period between 1997 and 2000 is =[0 to 4] [(0.18/3)t3+(0.16/2)t2 +2.64t]
number of notebooks sold over 4 year period between 1997 and 2000 is =[0 to 4] [0.06t3+0.08t2 +2.64t]
number of notebooks sold over 4 year period between 1997 and 2000 is
= [0.06*43+0.08*42 +2.64*4]- [0.06*03+0.08*02 +2.64*0]
number of notebooks sold over 4 year period between 1997 and 2000 is = 15.68 million units