Question

A certain strain of bacteria divides every two hours. If a colony is started with 70 bacteria, then the time t (in hours) required for the colony to grow to N bacteria is given by
t = 2 (log(N/70))/(log (2))
.
Find the time required for the colony to grow to three million bacteria. (Round your answer to two decimal places.)

Answer 1

Substitute 3 million in for N and solve.

Answer 2

would it be 29.60?

Answer 3

No, you rounded somewhere in the middle. Try not to round until the very end.

Answer 4

punch in log(3000000/2)

Answer 5

6.176

Answer 6

Don't round it, leave it in the calculator, then simply hit "times 2"
(It will say ANS * 2, or some similar)

Answer 7

No no! Don't do that :P
That's what I just warned against. You're rounding in the middle of the problem.

Answer 8

12.35

Answer 9

What? No.
Do you see the "log" button on your calculator?

Answer 10

yes i am using that!!!!!

Answer 11

Yes, but stop rounding in the middle of the problem, simply leave it in the calculator. It will be a very long number.

Then simply hit "times 2"

Answer 12

Then leave THAT result in the calculator and hit "divide log(2)"

Answer 13

\[t=2\frac{ \log(N/70) }{ \log(2) }\] is this how you're seeing the equation?

Answer 14

Yep.

Answer 15

Do you understand what I mean by "rounding in the middle" ?

Answer 16

Your answer is off by about 1. Which is significant. Because you rounded part way through solving.

Answer 17

not really... i've been putting the question directly into my calculator and am still getting 29.6045711

Answer 18

30.77449611 ...that is a closer approximation.

Answer 19

You're off by more than 1.

Answer 20

my calculator is not giving me that at all...

Answer 21

Okay, hit log(3000000/70)
DO NOT ROUND: What do you have?

Answer 22

4.632023215

Answer 23

Okay, now leave that in your calculator EXACTLY how it is. Now just hit "times 2"
It will read "ANS * 2" or something like that.

Answer 24

k

Answer 25

Now what have you?

Answer 26

9.264046429

Answer 27

Okay now leave that EXACTLY how it is and simply hit "divide log(2)"

Answer 28

now i got what you got!!!!! thanks!!!

Answer 29

There you go. See those little round offs in the middle of a problem don't SEEM like much, but they get really big really fast when dealing with large numbers. That's called error propagation. So always "round at the end".

Answer 30

could you help me with another similar one?

Answer 31

I'm running low on time, but post another thread and someone will help.

Answer 32

okay but thanks again!!