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28 Aug 2003, 13:32
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Q. In 1970 the production of mobile phones was .8 million. During
the 11 year period from 1970 to 1980 the production of mobiles
increased at a constant rate every year. If a total of 14.3 million
mobiles were produced during the period then what is the range of
the mobile phone production for the 11 year period.
I apologise for no answer selections, but can anyone solve?
My method
1970=.8
1971=.8x
1972=.8x^2
1973=.8x^3
....
1980=.8x^10
The sum of these will equal 14.3, but what next?
What we need to find is (.8x^10) - .8
Many thanks
the 11 year period from 1970 to 1980 the production of mobiles
increased at a constant rate every year. If a total of 14.3 million
mobiles were produced during the period then what is the range of
the mobile phone production for the 11 year period.
I apologise for no answer selections, but can anyone solve?
My method
1970=.8
1971=.8x
1972=.8x^2
1973=.8x^3
....
1980=.8x^10
The sum of these will equal 14.3, but what next?
What we need to find is (.8x^10) - .8
Many thanks
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28 Aug 2003, 14:57
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bufff... lets see, heres my reasoning:
lets call S=0.8+0.8*x+...+0.8*x^10
then S=0.8*((x^11)-1)/(x-1)=14,8
rearrenging we have
S=0.8*[[x*((x^10)-1)/(x-1)]+1]=14,8
thus 0.8*((x^10)-1)=14*(x-1)/x=14*(1-1/x)
we know that x>1, so the range asked is 0-14
lets call S=0.8+0.8*x+...+0.8*x^10
then S=0.8*((x^11)-1)/(x-1)=14,8
rearrenging we have
S=0.8*[[x*((x^10)-1)/(x-1)]+1]=14,8
thus 0.8*((x^10)-1)=14*(x-1)/x=14*(1-1/x)
we know that x>1, so the range asked is 0-14
