Tuesday

September 23, 2014

September 23, 2014

Posted by **George** on Sunday, November 9, 2008 at 1:57pm.

A few bacteria search for more food and space. They find three more syrup cans how much of a time reprieve are they given by this find? When will the new cans be depleated?

I can't figure out how to do these problems without being given the number of bacteria that fell into the can to begin with...is there a way to do it that I'm not seeing?

- Math Word Problem -
**Reiny**, Sunday, November 9, 2008 at 3:45pmI am a bit befuddled by this question.

According to your first part, we could say that the bacteria population is

N(t) = a(2)^(t/2) where N(t) is the number of bacteria and t is time in minutes after 6 am.

so at 6 am, t = 0, and N(0) = a(2)^0 = a

so we started with a bacteria

How many do we have at 6 pm?

that is 12 hours or 720 minutes, so t=720

N(720) = a(2)^36

= a(6.872 x 10^10) bacteria

then you ask "At what time does the syrup become half full?"

did you mean : At what time does the syrup can become half the capacity of the bacteria?

half of a(6.872 x 10^10) is a(3.436 x 10^10)

so we solve

a(3.436 x 10^10) = a(2)^(t/20)

notice the a drops out

I hope you know how to do logs.

log (3.436 x 10^10) = (t/20)log2

t/20 = log(3.436 x 10^10)/log2

t/20 = 35

t = 35(20) = 700 minutes, which would correspond to 5:40 pm

(At this point I said to myself, Duhhh!

since it doubled every 20 minutes, half the content must have been reached within the last doubling period, which of course is 20 minutes)

Give the last part a shot yourself, ok?

**Answer this Question**

**Related Questions**

AP Environmental Science - I have a word problem about exponential growth. The ...

Math,fraction word problem - a total of 9litres of orange syrup was poured ...

biology - There is a bacteria called botulism which will grow in anaerobic ...

Pre-Calc (exponential growth) - A COLONY OF BACTERIA IS GROWN UNDER IDEAL ...

Algebra 2 - Ordinary corn syrup contains dextrose sugar. A process called enzyme...

food - if a single bacterium on food has ideal conditions , approximately how ...

Math - Bacteria experiences exponential growth, increasing 17% every hour. If ...

chemistry - How can I convert 350mg/L into mg/kg with 22.28% moisture? You need ...

Math - Jessica purchased a bag of cat food. She feeds her cat 1 cup of cat food ...

Calculus - Under a set of controlled laboratory conditions, the size of the ...