Got Homework?
Connect with other students for help. It's a free community.
Here's the question you clicked on:
 0 viewing
soccergal12
Group Title
Peter's chickens got the bird flu and he is rying to stop the epidemic. He knows that the function
f(t) = 300 / ( 10 + 20e^(1.5t) )
describes the number of his chickens who are sick t weeks after the initial outbreak.
(a) How many chickens became sick when the flu epidemic has began?
I got 10/7 for the answer. does that seem right???
(b) In how many weeks will 100 chickens be sick?
(c) What is the maximum number of chickens that will become ill?
 2 years ago
 2 years ago
soccergal12 Group Title
Peter's chickens got the bird flu and he is rying to stop the epidemic. He knows that the function f(t) = 300 / ( 10 + 20e^(1.5t) ) describes the number of his chickens who are sick t weeks after the initial outbreak. (a) How many chickens became sick when the flu epidemic has began? I got 10/7 for the answer. does that seem right??? (b) In how many weeks will 100 chickens be sick? (c) What is the maximum number of chickens that will become ill?
 2 years ago
 2 years ago

This Question is Closed

rafabc02 Group TitleBest ResponseYou've already chosen the best response.3
For part (a) we just have to plug in t=0, so: 300/(10+20)=300/30=10 Part (b): Plut t=100 and solve. Part(c): Take the derivative and set it equal to zero.
 2 years ago

rafabc02 Group TitleBest ResponseYou've already chosen the best response.3
@soccergal12 Did that help?
 2 years ago

soccergal12 Group TitleBest ResponseYou've already chosen the best response.0
yes it did, thank you
 2 years ago

rafabc02 Group TitleBest ResponseYou've already chosen the best response.3
OK, awsome! Glad to help you!
 2 years ago

soccergal12 Group TitleBest ResponseYou've already chosen the best response.0
im just unsure about the derivative; i'm not sure how to do it entirely
 2 years ago

soccergal12 Group TitleBest ResponseYou've already chosen the best response.0
and in question b, aren't i finding t, not f(100) ?
 2 years ago

soccergal12 Group TitleBest ResponseYou've already chosen the best response.0
scratch that last question .. i'm just unsure about how to do the derivative : where do i begin?
 2 years ago

soccergal12 Group TitleBest ResponseYou've already chosen the best response.0
i got ( 9000e^1.5t ) / (10 + 20e^1.5t )^2
 2 years ago

rafabc02 Group TitleBest ResponseYou've already chosen the best response.3
You are right, about part (b), sorry about that, we have to do this: 100=300 / ( 10 + 20e^(1.5t) ) And solve for t Part (c): \[f(t) = 300( 10 + 20e^{1.5t} )^1\] so the derivative is: \[300*(1)*(10 + 20e^{1.5t} )^{2}*20e^{1.5t}(1.5)\]
 2 years ago

rafabc02 Group TitleBest ResponseYou've already chosen the best response.3
Which is the same as: \[\frac{9000e^{1.5t}}{(10+20e^{1.5t})^2}\]
 2 years ago

rafabc02 Group TitleBest ResponseYou've already chosen the best response.3
So you did it great! Any doubt?
 2 years ago

soccergal12 Group TitleBest ResponseYou've already chosen the best response.0
okay thanks! sorry i have another question about part b : to find t, i got down to e^1.5t = 7/20 ; could you do this question and let me know if you get the same answer? also, where do i go from here: do i ln both sides?
 2 years ago

rafabc02 Group TitleBest ResponseYou've already chosen the best response.3
\[100=\frac{300}{ ( 10 + 20e^{1.5t} )}\rightarrow10 + 20e^{1.5t} =\frac{300}{100}\] So then: \[20e^{1.5t}=20\] \[e^{1.5t}=1\]
 2 years ago

soccergal12 Group TitleBest ResponseYou've already chosen the best response.0
doesn't it equal 20^e −1.5t = 7 ?
 2 years ago

rafabc02 Group TitleBest ResponseYou've already chosen the best response.3
We start from here: \[100=\frac{300}{10+20e^{1.5t}}\] Then we have this: \[10+20e^{1.5t}=\frac{300}{100}\] So then, \[20e^{1.5t}=310=7\] You are right! Sorry about my confusion! But then, how do we solve it?
 2 years ago

rafabc02 Group TitleBest ResponseYou've already chosen the best response.3
I think that this function never reaches 100. Take a look here: http://www.wolframalpha.com/input/?i=100+%3D+300+%2F+%28+10+%2B+20e%5E%281.5t%29+%29
 2 years ago

soccergal12 Group TitleBest ResponseYou've already chosen the best response.0
so would i state that the function doesn't ever reach 100?
 2 years ago

rafabc02 Group TitleBest ResponseYou've already chosen the best response.3
I think so. You can see it on the graph. Any other doubt?
 2 years ago

Jemma6 Group TitleBest ResponseYou've already chosen the best response.0
I have this same question, but it has been changed to: f(t) = 300 / ( 15  20e^(0.07t) ) When I have this information though, the answer I get for part A is negative. That doesn't make sense. Can anyone help me figure out how to solve this with the changes made?
 2 years ago

soccergal12 Group TitleBest ResponseYou've already chosen the best response.0
I get a negative answer too, and my function has changed too. could anyone help us figure this out ?
 2 years ago

dumbcow Group TitleBest ResponseYou've already chosen the best response.0
this looks like a logistic function it approaches an upper limit as t goes to infinity the term "20e^(1.5t)" goes to 0 leaving 300/10 = 30 the maximum possible sick chickens is 30 it will never be 100 so part b) is never
 2 years ago
See more questions >>>
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.