A "Slick" problem

Algebra Level 2

John is studying a certain strain of bacteria to clean up an oil slick. He calculates that $2^{13}$ cells are necessary to complete the job. If he starts with one cell, and the bacteria colony divides every 15 minutes, how many hours will it take for the bacteria to complete the job?

The answer is 3.25.

2 solutions

Eamon Gupta
Apr 11, 2015

Since it starts with $2^{0} cell$ and it takes 15 minutes for the power to go up by 1, it will take $\frac{13}{4}hours$ to reach $2^{13} cells$ . Hence the time required is $\frac{13}{4}=\boxed{3.25}$ hours. $\square$

it should be 3.5 hours, as he starts with 1 cell and for one cell to become 2 it will take 15 mins in starting so as i think we need to add that 15 mins too.

Himanshu Goel - 5 years, 7 months ago

This should clarify:

$2^{time blocks}$ = # of cells produced

If he needs 1 cell ( $2^0$ cells), he starts with it, so 0 time blocks need to pass.

$(2^0 = 1)$

If he needs 2 cells ( $2^1$ cells), he starts with 1, so 1 time block to pass.

$(2^1 = 2)$

$therefore$

If he needs $2^{13}$ cells, he needs 13 blocks of time, which is 3.25 hours

Neil Smith - 5 years, 6 months ago

Good job Eamon! :)

John Daly - 6 years, 2 months ago

Shuvam Jaiswal
Apr 23, 2015

Starting with 1(2^{0}) , the division goes on till 2^{13}, each division requiring 15 minutes. Therefore, Total time required (in minutes) = 15 x 13 = 195 minutes = 3.25 hours.

it should be 3.5 hours as he had set 1 cell and for one cell to become two it takes 15 mins so we need to add that 15 mins also

Himanshu Goel - 5 years, 7 months ago

A "Slick" problem

The answer is 3.25.

2 solutions

0 pending reports