A community for students. Sign up today!
Here's the question you clicked on:
 0 viewing
mr.luna
 3 years ago
how do i set this up?! a bacteria culture initially contains 100 dells and grows at a rate proportional to its size. after an hour the population has incresed to 420.
a)find an expression for the number of bacteria after t hours.
b)find the number of bacteria after 3 hours
c)find the rate of growth after 3 hours
d)when will the population reach 10,000
mr.luna
 3 years ago
how do i set this up?! a bacteria culture initially contains 100 dells and grows at a rate proportional to its size. after an hour the population has incresed to 420. a)find an expression for the number of bacteria after t hours. b)find the number of bacteria after 3 hours c)find the rate of growth after 3 hours d)when will the population reach 10,000

This Question is Closed

mr.luna
 3 years ago
Best ResponseYou've already chosen the best response.0i have trouble converting it to numbers. here what i have so far and i working on more. i use the P(t)=P(0)e^kt

mr.luna
 3 years ago
Best ResponseYou've already chosen the best response.0i set the equation P(3)=100e^3k=420 i solved and got k=ln42/3

mr.luna
 3 years ago
Best ResponseYou've already chosen the best response.0is a [100e^[(ln42/3)(t)]

mr.luna
 3 years ago
Best ResponseYou've already chosen the best response.0b) i just plug in 3 for t to the equation in a) ?

mr.luna
 3 years ago
Best ResponseYou've already chosen the best response.0for d) i put equation a) equal to 10,000 right?

mr.luna
 3 years ago
Best ResponseYou've already chosen the best response.0im stuck on c) though. how do you do that?

victorarana
 3 years ago
Best ResponseYou've already chosen the best response.1I guess that you can derive the expression you got before to obtain dP/dt. And then you sustitute the value of 3 on it. .

mr.luna
 3 years ago
Best ResponseYou've already chosen the best response.0i got it down to 100(42^t/3) i dont how to dervie?

victorarana
 3 years ago
Best ResponseYou've already chosen the best response.1I think your initial conditions are wrong. You wrote P(3) = 420, and on the problem says P(1) = 420

victorarana
 3 years ago
Best ResponseYou've already chosen the best response.1\[420 = 100e^{k(1)}\]

mr.luna
 3 years ago
Best ResponseYou've already chosen the best response.0ok crap .yeah your right! good catch

victorarana
 3 years ago
Best ResponseYou've already chosen the best response.1\[P = 100e^{\ln(4.2)t}\]

victorarana
 3 years ago
Best ResponseYou've already chosen the best response.1if you derive you get: \[\frac{d}{dt}100e^{(\ln 4.2)k}= 100(\ln4.2)e^{(\ln 4.2)k}\]

victorarana
 3 years ago
Best ResponseYou've already chosen the best response.1sorry its t instead of k

mr.luna
 3 years ago
Best ResponseYou've already chosen the best response.0im trying to get waht you got for the derviative right now. its not coming out for me.

mr.luna
 3 years ago
Best ResponseYou've already chosen the best response.0instead of ln4.2 i get 4.2k

victorarana
 3 years ago
Best ResponseYou've already chosen the best response.1remember that \[\frac{d}{dx}e^{ax} = ae^x\]

victorarana
 3 years ago
Best ResponseYou've already chosen the best response.1Sorry i missed an "a" \[\frac{d}{dx}e^{ax}=ae^{ax}\]

mr.luna
 3 years ago
Best ResponseYou've already chosen the best response.0oh. ok. got it now. thanks
Ask your own question
Ask a QuestionFind more explanations on OpenStudy
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.