A manufacturer of light bulbs estimates that the fraction F(t) of bulbs that remain burning after t week is given by F(t)=e^(-kt) where k is a postive constant. Suppose twice as many bulbs are burning after 5 weeks as after 9 weeks.

Find k and determine the fraction of bulbs still burning after 7 weeks.

I can't figure out how to get k

all I have so far is 2(e^(-5k))=e^(-9k) but I'm beginning to question whether that is right

Question

A manufacturer of light bulbs estimates that the fraction F(t) of bulbs that remain burning after t week is given by F(t)=e^(-kt) where k is a postive constant. Suppose twice as many bulbs are burning after 5 weeks as after 9 weeks.

Find k and determine the fraction of bulbs still burning after 7 weeks.

I can't figure out how to get k

all I have so far is 2(e^(-5k))=e^(-9k) but I'm beginning to question whether that is right

anonymous · Answer

I did 2=e^(-9k)/e^(-5k) to get 2=e^(-4k) then took ln of both sides got ln2=-4k, idk if that is right

anonymous · Answer

im a tard shouldnt it be 2e^-9k=e^-5k ?

anonymous · Answer

yessss!

anonymous · Answer

then the answer makes sense now lol

anonymous · Answer

Lol Yess! it makes more sense xDDD :)

anonymous · Answer

did you get it or your still 

blah..Lol

anonymous · Answer

took my like a day to get this problem took you like 5 seconds

the answer is ln2/4 right after that the rest of the problem is cake

anonymous · Answer

YESS!!!! 

wow.. a day?

anonymous · Answer

well I went to sleep on it picked up in the morning

anonymous · Answer

which was 5 minutes ago lol

anonymous · Answer

oh. :p