Question

A bacteria culture initially contains 600 cells and grows at a rate proportional to its size. After 4 hours the population has increased to 690. Find the rate of growth after 9 hours.

Answer 1

confused
are you supposed to find the population after 9 hours?

Answer 2

the rate of growth, the population at that time is 821.715

Answer 3

what does 'rate of growth" at that time mean?

Answer 4

I have no idea, thought someone on here might know

Answer 5

do you have an example?

Answer 6

no

Answer 7

really? damn

Answer 8

let me google

Answer 9

ooh i have an idea
is this a calc course?

Answer 10

yes

Answer 11

if so, take the expression you got for the population
then take the derivative of it,
then plug in 9

Answer 12

did you write it as \[P(t)=A_0e^{rt}\] for some \(r\)?

Answer 13

i guess you must have, to find the population after 9 hours
of course \(A_0=600\) what did you get for \(r\)?

Answer 14

.0349404856

Answer 15

man you like decimals

Answer 16

so \[P(t)=600e^{.0349404856
t}\] right?

Answer 17

i would have rounded a bit, but no matter
find \[P'(t)=.0349404856\times 600e^{.0349404856
t}\] then find \[P'(9)\]

Answer 18

i am assuming your \(r\) is right
btw decimals or no, you should at least round the population to a whole number so it makes sense

Answer 19

yeah I know, it's just for some reason it won't except it as a whole number. It's kind of retarded

Answer 20

i get about \(28.7\)
http://www.wolframalpha.com/input/?i=.0349404856*600e^ {.0349404856+*9}

Answer 21

oops that won't work unless you copy and paste
http://www.wolframalpha.com/input/?i=.0349404856*600e^%28.0349404856+*9%29

Answer 22

it won't accept a whole number for the population? lol

Answer 23

Yeah, I know. But thank you for the help

Answer 24

yw
hope that answer was right, should be so long as your \(r\) is right

Answer 25

it was

Answer 26

whew

Answer 27

all the problem was interpreting the question
thank god for google