Question

A store had 100 t-shirts. Each month, 30% of the t-shirts were sold and 25 new t-shirts arrived in shipments. Which recursive function best represents the number of t-shirts in the store, given that f(0) = 100?

f(n) = f(n - 1) • 0.3 + 25, n > 0
f(n) = 100 - f(n - 1) • 0.3 + 25, n > 0
f(n) = f(n - 1) • 0.7 + 25, n > 0
f(n) = 100 - f(n - 1) • 0.7 + 25, n > 0

Answer 1

i am just stuck on this one @Miracrown

Answer 2

i was thinking A

Answer 3

or D

Answer 4

ya there?

Answer 5

Yea, sorry my connection was acting fuzzy ...

The best way to solve this is to try it out:
If the store starts with 100 t-shirts, how many would there be after 1 month, according to the problem?

Answer 6

you would have 95, right?

Answer 7

Mhm

Answer 8

cause 100*0.3 = 30 so 30 shirts where sold, so you ahve 70 hirts. 25 more come in so 95

Answer 9

So the question becomes: which of these functions get us 95 after 1 month?
If we plug in 100 for each of the f(n - 1)'s

Answer 10

oh so it would be B?

Answer 11

that is what I was thinking after what I said

Answer 12

So... if we replace f(n - 1) with 100 in answer choice A...
would we get 95?

Answer 13

oh wait hold on

Answer 14

B gets us 95, yes. Do any others get us 95 as well, besides B?

Answer 15

A = 55
B = 95
C = 95
D = 55

Answer 16

So B and C get us 95

Answer 17

right

Answer 18

To figure out which one it is, let's do it again.
Let's start with 95, and see how much we have after the 2nd month ...

Answer 19

with only B and C?

Answer 20

How much would that be, according to the problem?

Answer 21

according to the wording in the problem the one where 30% are sold and 25 others are added, If we started with 95, how much would we get after this process?

Answer 22

91.5

Answer 23

oohh it's C

Answer 24

C = 91.5 when plugging in 95 as f(n-1)

Answer 25

YES!

Answer 26

yay thanks so much i loved how you explained n stuff <3

Answer 27

Haha no worries :)

Answer 28

made me really understand what was going on

Answer 29

Anytime <3