Advanced Functions test question

[Sorry!]

A bacteria doubles every 15h find when it will be at 1/16th of its present amount.
not sure if there were more stuff stated but that's basically the jist of it.

i'm assuming y=b(2)^(x/15) is the doubling equation


not so sure how to solve it was going to just put in times 1/16 for the exponent but then i noticed that it was too little steps and the question was out of 4

(it was on a advanced functions test i just had today lol)

 

[Dick]

Ok, so let y(x)=b*2^(x/15). If the present time is x=0, you want to solve y(x)=y(0)/16. Put your form into that and solve for x.

 

[Sorry!]

yeah i did that at first (i think it's what your talking about) and it was like

y(0)/16=2^(x/15)

2^(0)/16=2^(x/15)

1/16=2^(x/15)

2^(-4)=2^(x/15)
-4=x/15
-60=x

and i lost a mark cause the negative (i think...) another student instead subbed 1/16 for b and ended up with +60 and got full marks, just wondering if anyone knows why?
i only just looked at the question now.
sucks cause i think that mine was just from different reference...

 

[Dick]

y(0)=b. So your first equation should read b/16=b*2^(x/15) and the b cancels. Other than that I'd call the solution fine. If the population is doubling every 15h then the time when it was 1/16 of it's current size was 60 hrs in the past.

 

[Sorry!]

ooooooooohh maybe i lost a mark for not fully solving for y(0) before subbing ... forgot completely about the b tbh.

thanks man :D