A store had 175 cell phones in the month of January. Every month, 10% of the cell phones were sold and 10 new cell phones were stocked in the store.
Which recursive function best represents the number of cell phones in the store f(n) after n months?
f(n) = 175 - 0.9 • f(n - 1) + 10, f(0) = 175, n > 0 f(n) = 0.1 • f(n - 1) + 10, f(0) = 175, n > 0 f(n) = 175 + 0.9 • f(n - 1) + 10, f(0) = 175, n > 0 f(n) = 0.9 • f(n - 1) + 10, f(0) = 175, n > 0
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10% of the cell phones were sold
if you sell 10% of the phones, what percent do you have left ?
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yes, and you can write 90% as 0.9 (90% means 90/100)
if you call the number of phones f(n)
then you will have 0.9*f(n)
then 10 new cell phones were stocked
that means add 10:
0.9*f(n) + 10
that is the number of phones for the next month, i.e. for f(n+1)
thus: f(n+1) = 0.9 f(n) + 10
of course, you need a starting number of phones at n=0
f(0)= # of phones you start with.
175 cell phones in the month of January
so I would say f(0)= 175