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soccergal12
 3 years ago
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?
soccergal12
 3 years ago
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?

This Question is Closed

rafabc02
 3 years ago
Best ResponseYou've already chosen the best response.3For 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.

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

soccergal12
 3 years ago
Best ResponseYou've already chosen the best response.0yes it did, thank you

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

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

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

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

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

rafabc02
 3 years ago
Best ResponseYou've already chosen the best response.3You 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: \[300*(1)*(10 + 20e^{1.5t} )^{2}*20e^{1.5t}(1.5)\]

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

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

soccergal12
 3 years ago
Best ResponseYou've already chosen the best response.0okay 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?

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

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

rafabc02
 3 years ago
Best ResponseYou've already chosen the best response.3We 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?

rafabc02
 3 years ago
Best ResponseYou've already chosen the best response.3I 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

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

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

Jemma6
 3 years ago
Best ResponseYou've already chosen the best response.0I 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?

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

dumbcow
 3 years ago
Best ResponseYou've already chosen the best response.0this 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
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