Question

The colour of some clothing fades overtime when washed. Suppose a pair of jeansfades by 5% with each washing. To the nearest wash, how many washes would it take so that only 25% of the original colour remains in the jeans?
1. first term =
2. r =
3. tn =
4. n =

I know that tn is 25 because that's the term that they're asking for but I cna't figure out the "r"... I thought it was 19/20 because when 5% fades, 95% of the color is left but I got it wrong.

Answer 1

you want:

.95^n = .25
take log of both sides

nlog.95 = log.25
n = log.25/log.95 = 27.0268..

= appr 27 washings

or

start with 100% colour
after 1 washing ---- 95% left
after 2 washings --- .95(.95) left
after 3 washings --- .95(.95)^2 left
....
after n washings ------ .95(.95)(n-1) left , should be .25

so .95(.95)^(n-1) = .25
.95^n = .25 , which is the same equation I started with

checking my answer of 27 washings
amount left over = .95(.95)^26 = .25034
or appr 25%

Answer 2

don't make confusing, because if u look at the sequence its 100, 95, 90.25, 85.7375
first term is 100 this is the original color and second term is 95 and this is second term but first hand wash if you follow the pattern then for term three number of hand wash is two and for term four number number of hand wash three and so on . hence for this situation 10 washings for 11th term : t11=100(.95)^10=59.87
and we have happy ending