The number of bacteria in a jar triples every 20 seconds....

[markus42]

The number of bacteria in a jar triples every twenty seconds. After three minutes 275,562 bacteria are in the jar. How many bacteria werre in the jar at the beginning of the experiment?

 

[stapel]

The number of bacteria in a jar triples every twenty seconds. After three minutes 275,562 bacteria are in the jar. How many bacteria werre in the jar at the beginning of the experiment?

I'm not sure why this exercise is being assigned in an advanced algebra course, nor why you are unable even to get started...? This only requires grade-school arithmetic! :shock:

How many seconds are in three minutes? (Hint: Multiply.)

So how many twenty-second periods are in three minutes? (Hint: Divide.)

Counting backwards from the end, what was the bacteria load twenty seconds before the end of three minutes? That is, twenty seconds before the ending point, how many bacteria were there? (Hint: Divide by two.)

Counting backwards another twenty seconds, how many bacteria where there at that point? (Hint: Divide by two again.)

Continue until you are at the beginning of the three minutes. (Hint: Keep dividing by two, keeping track of the twenty-second periods as you go.)

If you get stuck, please reply showing how far you got in following the step-by-step instructions. Thank you!

Eliz.

 

[Deleted member 4993]

The number of bacteria in a jar triples every twenty seconds. After three minutes 275,562 bacteria are in the jar. How many bacteria werre in the jar at the beginning of the experiment?

Assume in the begining population was \(\displaystyle P_0\)

Then population after 'n' units of 20 seconds

\(\displaystyle P = P_0 \cdot 3^n\)

You know n (units of 20 secs in 3 minutes), you know \(\displaystyle P\) (=275562) find \(\displaystyle P_0\)