Exponential and Logarithmic Functions

[Lurid]

Can anyone check my work? I'm doubtful of my answer.

Homework Statement

The bacteria in a 4-liter container double every minute. After 60 minutes the container is full. How long did it take to fill half the container?

Homework Equations

I used:

F = A × 2⁶⁰
(1/2)F = A × 2^x

F is "full", A is the starting amount of bacteria, and x is time in minutes.

The Attempt at a Solution

(1/2)(A × 2⁶⁰) = A × 2^x

(1/2)(2⁶⁰) = 2^x
2^60-1 = 2^x
60 -1 = x
59 minutes = x

 

[spaghetti3451]

Well done!

Now that you know the answer, you can understand that you could have got the answer by inspection. If the bacteria doubles every minute, then the container MUST HAVE BEEN half full after 59 minutes. IF ANF ONLY IF THIS HAPPENS can you double the bacteria and get the full container after the next minute (i.e. after 60 minutes).

 

[Lurid]

Thanks!

Oh, wow. I never though of it that way! That would have saved a lot of work, haha.

 

[Lurid]

Thanks!

Oh, wow. I never though of it that way! That would have saved a lot of work, haha.

 

[Curious3141]

This is one of those well known trick questions. Sometimes appears on informal "for fun" IQ tests.