Question

In 1934 the biologist G.F. Gause placed 20 paramecia in 5 cc of saline solution with a constant amount of food, and measured the population of the colony on a daily basis. he found that the population f(t) after t days

f(t) = 1049/(1+(e^5.4094-1.0235t))

determine the maximum size of the colony

Answer 1

lets find the derivaitve

Answer 2

f'(T)=1049(e^5.4094-1.0235t) what is next step?

Answer 3

set it to zero

Answer 4

i got t=5.285 how can i find the maximum size of the colony?

Answer 5

now determine whether the sign of the derivative changes from + to -, this will determine if there is a maximum at this value of x

Answer 6

do you mean just plug in 5.285 for t in the equation?

Answer 7

it would behoove you to check if this is indeed a maximum. But yeah, just plug that into your ogrinal function

Answer 8

f'(5.285)=524.5 is it the maximum ?

Answer 9

plug it into the original funtion to find the y value

Answer 10

f(X)=524.5 it isnt f'(X)

Answer 11

okay then your right :)

Answer 12

is that all?

Answer 13

thats all your question asked

Answer 14

Thank you so much