I’d like to make some extra cash so I decided to release the kPhoneX to compete

ID: 3146748 • Letter: I

Question

with Samsung and Apple. “It’s the most fantastic smartphone ever. Trust me! All others

are sad!” In the week since the launch date on 10/31/2017 I have sold an estimated 17

units. ( P_1 =17 ) and suppose that sales for my new kPhone1 grows at a steady rate of

8.4% per week after launch.

(a) Show HOW to find a recursive formula for the sequence of kPhoneX sales {P_n}

where n is the number of weeks after launch and n >= 1.

(b) Show HOW to use iteration to make an educated guess at an explicit formula for

the sequence, {P_n} .

ending on Tuesday 12/26/2017

launch date is 31/10/2017

in first week 17 items are sold

{P_1}=17

and the sales grows at a steady rate of 8.4%per week after launch

therefore {P_2}={P_1} +{P_1}*8.4/100

{P_2}={P_1} (1+8.4/100)

similarly

{P_3}={P_2}+{P_2}*8.4/100

which gives

{P_3}={P_1}(1+8.4/100)^2

therefore {P_n} ={P_1} (1+8.4/100)^n-1

between 10/31/2017 and 12/26/2017 there are 8 weeks

therefore putting n=8 in formula we get

{P_8}=17(1+8.4/100)^7

=29.89,which is approximately 30

therefore kphone1 sales for the week ending on tuesday 12/26/2017 is 30

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