Question

a cell of the bacterium escherichia coli in a nutrient-broth divided into two cells every 20 min. Suppose that there are initially 500 cells . Find the number of cells after t hours. How many cells will there e after 8 hours?

Answer 1

Oh let me think...isn't that equation
\[A=A _{0}e ^{kt}\]

Answer 2

yes

Answer 3

but I use a instead of e since the equation with e is for "continuously" questions

Answer 4

So first we need to find k. And we know that if the original amount is 1, in 1/3 hour, there will be 2

Answer 5

Could you post your equation?

Answer 6

A=A0 a ^ik

Answer 7

What is a?

Answer 8

What does it represent?

Answer 9

Would it be 2 in this example?

Answer 10

And i is the time period?

Answer 11

I think it represents if the question is a half life question or doubling time, so if its half life, then it would be 1/2, so i think in this it would be 2 since the bacteria doubles

Answer 12

\[2=1(2)^{\frac{1}{3}k}\]

Answer 13

t is the time, its like the x-value . and i is the doubling time

Answer 14

ok, so why would I not use the 500 initial amount yet, because when I did it i used 500 instead of 1 to find the equation

Answer 15

\[\ln 2=\frac{1}{3}k \ln 2\]

Answer 16

k=3

Answer 17

\[A=500(2)^{8(3)}\]
\[A=8,388,608,000\]

Answer 18

every time i sub 8 into the equation i don't get the answer you have, which is the right answer

Answer 19

Did you get 3 for k?

Answer 20

yes

Answer 21

Did you do 2^24 first?

Answer 22

And then times 500?

Answer 23

no. I did the same questions in another math class and I was able to put the whole equation into my cal and it would give me the right answer, but now i get the wrong one

Answer 24

I don't know about your calculator but I know you do powers first. Do do 2^24 and take that answer times 500

Answer 25

ok. Could you answer another question?

Answer 26

Possibly

Answer 27

The count in a bacteria culture was 5000 after 15 min and 40 000 after 1 hour. What was the initial size of the culture. The two equations I came up with are 5000=A(2)^1/4t and 40000=A(2)^t

Answer 28

\[40000=5000(2)^{\frac{3}{4}k}\]

Answer 29

Find k

Answer 30

how did you get your equation, because my teacher said to either make the two equation equal each other and solve for k, or use substitution and when I did both i got wrong answers

Answer 31

If there were 5000 after 15 minutes, there were 10,000 after 30 minutes, 20,000 after 45 minutes, and 40,000 after 60 minutes. So if we take 40,000 for the final amount and 5000 for the beginning amount, and 3/4 hour for the time, we have the equation I posted.

Answer 32

The problem I see with your equations is that you don't know what k is.

Answer 33

If you wanted two equations you could write:
\[5000=A _{0}(2)^{\frac{1}{4}k}\]
and
\[40000=A _{0}(2)^{1k}\]

Answer 34

how would I solve it if I use substitution, because when I was doing it I was dividing out the 2

Answer 35

I would divide the second equation by the first:

Answer 36

\[\frac{40,000}{5,000}=\frac{A _{0}(2)^{1k}}{A _{0}(2)^{\frac{1}{4}k}}\]

Answer 37

\[8=2^{\frac{3}{4}k}\]

Answer 38

Then solve for k

Answer 39

would the 2 in the two equations not cancel out?

Answer 40

After you have k, you can find A_0 by substitution

Answer 41

No. When you do this problem:
\[\frac{x^8}{x^3}\]
do the x's cancel out?

Answer 42

no

Answer 43

Then why would the 2's cancel out?

Answer 44

i don't know. Sorry, i'm thinking of the 2 without the exponent. I'm sorry. I understand why now

Answer 45

could you stay around if i have another question

Answer 46

Did you get this one finished?

Answer 47

almost, it has sub-parts . working on it now

Answer 48

one of the sub-parts asks to find the population after t hours, the answer is 2500(16)^t

Answer 49

i have 2500(2)^4t

Answer 50

would they both be right?

Answer 51

I don't understand why you have 16 for the base in the one equation.

Answer 52

What did you get for k?

Answer 53

the answer at the back of my book has 16 as the base, I got 4 for k

Answer 54

And I take it 2500 is the beginning amount. The reason they have 16 for the base is that they incorporated the constant k into the base:

Answer 55

\[A=2500(2)^{4t}=2500(2^4)^t=2500(16)^t\]

Answer 56

would my answer of 2500 (2)4t be right?

Answer 57

Yes. They are the same thing.

Answer 58

Don't you understand what I just posted?

Answer 59

I did, I just need to make sure I'm doing it right because I suck at word problems. I'm sorry for being so annoying..

Answer 60

It's ok.

Answer 61

one of my questions says that the world population doubles every 35 a. What does it mean by a, I tried to look it up but I didn't find anything. Does it mean years