Open study

is now brainly

With Brainly you can:

  • Get homework help from millions of students and moderators
  • Learn how to solve problems with step-by-step explanations
  • Share your knowledge and earn points by helping other students
  • Learn anywhere, anytime with the Brainly app!

A community for students.

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

Mathematics
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

Get this expert

answer on brainly

SEE EXPERT ANSWER

Get your free account and access expert answers to this and thousands of other questions

i 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
so P(0)=100 P(3)=420
i set the equation P(3)=100e^3k=420 i solved and got k=ln42/3

Not the answer you are looking for?

Search for more explanations.

Ask your own question

Other answers:

is a [100e^[(ln42/3)(t)]
b) i just plug in 3 for t to the equation in a) ?
for d) i put equation a) equal to 10,000 right?
im stuck on c) though. how do you do that?
I guess that you can derive the expression you got before to obtain dP/dt. And then you sustitute the value of 3 on it. .
i got it down to 100(42^t/3) i dont how to dervie?
I think your initial conditions are wrong. You wrote P(3) = 420, and on the problem says P(1) = 420
\[420 = 100e^{k(1)}\]
so, \[k = \ln4.2\]
ok crap .yeah your right! good catch
\[P = 100e^{\ln(4.2)t}\]
if you derive you get: \[\frac{d}{dt}100e^{(\ln 4.2)k}= 100(\ln4.2)e^{(\ln 4.2)k}\]
sorry its t instead of k
im trying to get waht you got for the derviative right now. its not coming out for me.
what did you get?
instead of ln4.2 i get 4.2k
remember that \[\frac{d}{dx}e^{ax} = ae^x\]
Sorry i missed an "a" \[\frac{d}{dx}e^{ax}=ae^{ax}\]
oh. ok. got it now. thanks
You're welcome.

Not the answer you are looking for?

Search for more explanations.

Ask your own question