Question

Find the rate of growth after 8 hours. (Round your answer to three decimal places.)

Answer 1

@zeenat please post the complete question

Answer 2

0kay

Answer 3

A common inhabitant of human intestines is the bacterium Escherichia coli. A cell of this bacterium in a nutrient-broth medium divides into two cells every 20 minutes. The initial population of a culture is 65 cells.
(a) Find the relative growth rate. (Assume t is measured in hours.)
(b) Find an expression for the number of cells after t hours.
(c) Find the number of cells after 8 hours.
(d) Find the rate of growth after 8 hours. (Round your answer to three decimal places.)
(e) When will the population reach 20,000 cells? (Round your answer to two decimal places.)

Answer 4

Initial population is 65. It divides into two cells after every 20 minutes so
the population doubles every 20 minutes. Do you understand this?

Answer 5

yeah i do,tnxx

Answer 6

@zeenat Let the population by y after t minutes. Can you figure out what's the relation between y and initial population 65. ?
Remember that after 20 minutes population will be 65*2=130
after 40 minutes it'll be 130*2=260.

Answer 7

oh yeah, i do, i know what to do now. tnx to you!

Answer 8

@zeenat tell me what's the relation?

Answer 9

i tried this t = 65(8^t)In8 which is 8 = 65(8^8)In8... its giving me 2267670593.769, and ts wrong.

Answer 10

please don't ask me anything, i seriously dont know maths :D

Answer 11

@zeenat I'll help you but tell me how did you get 8?

Answer 12

It's doubling so there should be 2 involved, shouldn't be?

Answer 13

@zeenat I'm here, tell me whenever you need help

Answer 14

as in how 2 involve? i want you to write it how i will understand. thanks,am really bad in calculus

Answer 15

Okay
We have initial population as 65
and population after t minutes
\[\large y=65 \times 2^{\frac{t}{20}}\]
so we can see after 20 minutes it's
\[\large y=65 \times 2^{\frac{20}{20}}=65\times 2=130\]
so this is our equation of the population growth. Now you try the parts if you get stuck, do let me know:)

Answer 16

i dont know what to do, *sad face*

Answer 17

@zeenat what don't you understand?

Answer 18

Let's begin part by part. OK?

Answer 19

@zeenat I'm waiting for your response?

Answer 20

okay am here

Answer 21

answer for a) is In8
b) 65(8^t)
c) i inserted 8 in to t.. i got 1090519040

Answer 22

and part e: a(t) = 20 000
20 000 = 65*8^t
4000/13 = 8^t
t = log_8(4000/13)
t = 2.755114...

Answer 23

@zeenat brb

Answer 24

@ash2326 okay

Answer 25

I'm back!!

Answer 26

Oh one thing if t is measured in hours then in 60 minutes the population will increase by 8 , so
\[y=65\times 8^t\]
that's why there is 8. Do you understand this. Sorry I made a mistake

Answer 27

its okay, yeah i know that.

Answer 28

Now the rate of increase
\[\frac{dy}{dt}=\frac{d}{dt}65 \times 8^t\]
So we get
\[\frac{dy}{dt}=65 \times 8^t \times \ln 8\]
a) this is the solution for part a
b) \[y=65 \times 8^{t}\]
Can you try the other parts?

Answer 29

yeah i did all that but, d) is another story

Answer 30

put t=8 in
\[\frac{dy}{dt}=65 \times 8^{t} \times \ln 8\]

Answer 31

dy/dt at t=8 is your answer

Answer 32

okay lemme try

Answer 33

*wheww*

Answer 34

What's up?

Answer 35

am so tired, thank God am done

Answer 36

Good:D Take rest now:D

Answer 37

lol, Thanks so much!! i don't know how to thank you, hope you understand :D

Answer 38

Yeah, :D I'm glad to help:D
And
\[\large Welcome\ To\ Open\ Study:)\]

Answer 39

THANK YOU

Answer 40

you will teach me how to do this thing nxt tym...

Answer 41

Cool:D I'll teach you :)

Answer 42

okay, see you when i get stuck again,lol