Question

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?

Answer 1

(A) f(n) = 175 - 0.9 * f(n - 1) + 10, f(0) = 175, n > 0
(B) f(n) = 0.1 * f(n - 1) + 10, f(0) = 175, n > 0
(C) f(n) = 175 + 0.9 * f(n - 1) + 10, f(0) = 175, n > 0
(D) f(n) = 0.9 * f(n - 1) + 10, f(0) = 175, n > 0

Answer 2

so initially at time 0, n=0, f(n) = 175 phones

Answer 3

over a month 10% of them were sold, and 10 new ones were added

0.9*f(n-1) + 10

90% of the last value, plus 10

Answer 4

then when n increases to the next month, it will still be 90% of the last months still here , plust 10 new ones

Answer 5

recursive means that it will use the last value in the new equation, like, n=2 is used in figuring out the third month
n=3 used to figure out the 4th month,
all you need to know , is the initial value n=0, f(0)=175, and all the next months can be calculated

Answer 6

(D) f(n) = 0.9 * f(n - 1) + 10, f(0) = 175, n > 0

Answer 7

Yeah D was what I was going with first as well.

Answer 8

if you put in n=1, the first month

f(1) = 0.9* f(1-1) + 10
f(1) = 0.9*f(0) + 10

they say f(0) = 175

f(1) = 0.9*175 + 10

Answer 9

then that value for f(1), is used when you find f(2)

Answer 10

f(2) = 0.9*f(2-1) + 10
f(2) = 0.9* f(1) + 10

see the recursion?

Answer 11

f(3) will use the value for f(2)
f(4) will use the value for f(3)
.
.
.so on

Answer 12

THANK YOU SO MUCH FOR HELPING ME UNDERSTAND!! :)

Answer 13

you are welcome, anytime :)