Question

Medal and fan- of course. I answered the question with correct answers.
thanks @sangya21

During a research experiment it was found that the number of bacteria in a culture grew at a rate proportional to it's size. At 8:00 AM there were 2,000 bacteria present in the culture. At noon, the number of bacteria grew to 2,800. How many bacteria will there be by midnight?


During a research experiment it was found that the number of bacteria in a culture grew at a rate proportional to it's size. At 10:00 AM there were 3,000 bacteria present in the culture. At noon, the number of bacteria grew to 3,500. How many bacteria will there be by midnight?

Answer 1

\[P(t)=P _{0}e ^{kt}\]

Answer 2

I could do it myself but I don't enjoy interest formulae and exponential growth problems.

Answer 3

let time be at x
and no. of bacteria be y
slope of line = (2800 - 2000)/ (12-8)
m = 800/4
m = 200
rate of growth is 200 bacteria per hour
so from noon to midnight, there are 12 hours,
200 * 12= 2400
2400 more bacteria will be there

Answer 4

becuz 4 4 hrs it increases 800 so 800/4 right

Answer 5

correct

Answer 6

ok. I'm sorry for being lazy.

Answer 7

I'll probalby have some more problems so I might tag you.

Answer 8

Okie dokie

Answer 9

just remember to close this question

Answer 10

2000+2400=4400 for final answer

Answer 11

of course. im not new to openstudy.

Answer 12

oops.
2800+2400=5200

Answer 13

ugh. corect answer is 7,683.

Answer 14

I pressed similar excersise for a second chance.

Answer 15

During a research experiment it was found that the number of bacteria in a culture grew at a rate proportional to it's size. At 10:00 AM there were 3,000 bacteria present in the culture. At noon, the number of bacteria grew to 3,500. How many bacteria will there be by midnight?

Answer 16

^^^new question

Answer 17

2800+2400

Answer 18

how will u approach this question?

Answer 19

using the equation:

\[3500=3000(e ^{2k})\]

Answer 20

i skipped a whole bunch of steps`

Answer 21

im in College Algebra btw

Answer 22

Okk. I actually dont remember this equation so I take long route

Answer 23

\[\ln\frac{ 7 }{ 6 }=\ln(e ^{2k})\]

Answer 24

by using camcellation property f logs
\[\ln \frac{ 7 }{ 6 }=2k\]

Answer 25

*of

Answer 26

*cancellation

Answer 27

good. :)

Answer 28

ln(7/6)=0.15415
I'm rounding here but I won't round in the actual calculations.

Answer 29

then u divide by 2
k=0.077

Answer 30

so from 10:00 to noon is 2 hours. noon to midnight is 12. so total time is 14.`

Answer 31

the ` symbol is from me trying to press the tab for tab-enter

Answer 32

so your total no. of bacteria will be????

Answer 33

\[P(14)=3,000(e ^{14k})\]

Answer 34

plugging in k.

Answer 35

P(14)=3,000(2.941897)

Answer 36

P(14)=8826

Answer 37

btw this is for anyone who needs help.

Answer 38

thats why i solved it here

Answer 39

it is correct!

Answer 40

I have no idea why I wrote fan. ok, @sangya21 is fanned
-_-^-^-_-^-^-_-^-^-_-^-^-_-^-^-_-^-^-_-^-^-_-^-^-_-^-^-_-^-^-_-^-^

Answer 41

^^^those are my mixed emotions.

Answer 42

anytime and your welcome. :)

Answer 43

thanks sooo much forever