gnment Scoring our best submission for each question part is used for your score

Question

gnment Scoring our best submission for each question part is used for your score. -0.54 points HPreCale5 55.072 0'8 Submissions Used Between 1996 and 2004, the number of subscribers to cell-phone plans has g In 1996 there were 41,098,000 subscribers and in 2004 there were 177.419,000. (This problem deals with functions of My No (a) What is the continuous ous growth rate of the number of cell-phone subscribers? (Round your answer to four decimal places.) of the (b) In what year were there 70,000,000 cell-phone subsc (c) Assuming that this rate continues, in what year will there be 330 ,000,000 subscribers? (d) In 2007 the population of was approx a country was approximately 300 million. 1s your answer to part (c) realistic? Submit Answec Save Progress ss View Previous Question Question 24 of 23 Home tMy Assigoments Extension Reqlast TOSHIBA . DEL HONNE END

Explanation / Answer

Ans(a):

f(x)=Pe^{kx}
Say year 1996 corresponds to x=0
then year 2004 means x=8
Given that in 1996 , there were 41098000 subscribers
so that means if x=0 then f(x)=41098000
plug that into given equation

41098000=Pe^{k*0}
41098000=P*1
41098000=P

then given formula changes to
f(x)=41098000e^{kx}...(i)

Given that in 2004 , there were 177419000 subscribers
so that means if x=8 then f(x)=177419000
plug that into equation (i)

177419000=41098000e^{k*8}
177419000/41098000=e^{k*8}
ln(177419000/41098000)=8k
1.46255470822=8k
0.182819338528=k
Hence required answer is k=0.1828

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Ans(b):

Now we have to find x when f(x)=70000000
plug that into (i)
70000000=41098000e^{0.1828x}
70000000/41098000 =e^{0.1828x}
ln(70000000/41098000) =0.1828x
0.532535783532 =0.1828x
2.91321544602=x
which is approx 3
then corresponding year will be 1996+3=1999

Hence final answer is 1999.

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Ans(c):

Now we have to find x when f(x)=330000000
plug that into (i)
330000000=41098000e^{0.1828x}
330000000/41098000 =e^{0.1828x}
ln(330000000/41098000) =0.1828x
2.08313319594 =0.1828x
11.3956958202=x

which is approx 11
then corresponding year will be 1996+11=2007
Hence answer is year 2007

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Ans(d):

330000000 means 330 million which is almost same as 300 million So Yes my answer to part c) is realistic.

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