The color of some clothing fades over time when washed. Suppose a pair of jeans fades by 5% with each washing.

Question:
How many washings would it take so that only 25% of the original color remains in the jeans?

Question

The color of some clothing fades over time when washed. Suppose a pair of jeans fades by 5% with each washing.

Question:
How many washings would it take so that only 25% of the original color remains in the jeans?

anonymous · Answer

$$25 = 100(0.95)^{n-1}$$

anonymous · Answer

$$.25=(.95)^x$$ solve for x

anonymous · Answer

I don't get it, I need to solve for n

amistre64 · Answer

$$f_n=f_{n-1}-f_{n-1}(.05)$$

$$f_n=f_{n-1}(1-.05)$$

$$f_n=f_{n-1}(.95)$$

$$f_n=f_0(.95)^n$$

anonymous · Answer

Still doesn't make sense to me.

anonymous · Answer

Can you show steps of manipulation?

amistre64 · Answer

those are the steps ....

where do you get lost in them?

amistre64 · Answer

since we do not have your material to guide us; we just got to take a blind stab at it

anonymous · Answer

But i did give you info, it is a geometric sequence question

anonymous · Answer

$$T_{n}=T _{1}(r)^{n-1}$$

amistre64 · Answer

thats what we got; but my books always started at n=0, not n=1

anonymous · Answer

$$25 = 100(0.95)^{n-1}$$

amistre64 · Answer

divide off the 100

anonymous · Answer

$$0.025 = (0.0095)^{n-1}$$

amistre64 · Answer

dont add the superflous zeros

amistre64 · Answer

25/100 = .95^(n-1)

.25 = .95^(n-1)

which is what satellite started out with

amistre64 · Answer

ln both side

ln.25 = ln(.95^(n-1))

ln.25 = (n-1) ln(.95)

ln.25/ln(.95) = n-1