If the concentration, c(t), where c is in grams/liter, and t is in minutes, of a chemical changes according to the equation c'(t) = (0.7)c(t)[12 - c(t)], find the concentration c(t) for which the reaction rate is a maximum. c(t) =
2006-07-20 06:15:33 · 10 answers · asked by Olivia 4 in Education & Reference ➔ Higher Education (University +)
c(t)=12
No, it is not difficult if the function is well defined.
Let c(t) be the function in question, then find c(t) when c'(t)=0. The slope will be zero at the point where the function is min or maximum.
c'(t) = (0.7)c(t)[12 - c(t)]=0
[12 - c(t)]=0 then
c(t)=12 and the other value for c(t)=0 but may just as be undefined for our purpose.
Further, to test if one indeed has a minimum or a maximum, a second derivative is taken and the test value (in our case c(t)=12 is substituted.
c"(t)=12-2c(t)=12-24=-12 so at c(t)=12 we have c"(t)<0.
Since c"(t)<0 we have a maximum.
I hope that tickles you fancy :)
2006-07-20 10:11:29 · answer #1 · answered by Seductive Stargazer 3 · 0⤊ 2⤋
2
2006-07-20 06:18:24 · answer #2 · answered by Pal G 2 · 0⤊ 0⤋
Yep the guy is Perelman yet he did not quit his activity to artwork in this subject. He grew to become right into a traveling professor at UC Berkeley a jointly as in the past and greater at the instant he labored in a Russian institute in St. Petersburg. He very at the instant quit his activity as a results of his dissatisfaction with the mathematical community's loss of a solid reaction to what he considers an attempt to downplay his contributions to the evidence via yet another universal mathematician named Yau. As for the Nobel of arithmetic, yep Fields medal is in simple terms that and slightly greater, however the reason of the shortcoming of a Nobel for arithmetic has not something to do along with his spouse cheating Nobel. truthfully Nobel did not have a spouse. maximum historians have faith that Nobel in simple terms did not locate arithmetic clever sufficient to commit an award to.
2016-11-02 10:09:42 · answer #3 · answered by ? 4 · 0⤊ 0⤋
given the c'(t), you just need to set c'(t) = 0 to find the optimized value of c(t)
0.7(c(t))(12-c(t))=0
0.7(c(t))=0, 12-c(t)=0
c(t)=0, c(t)=12
therefore, c(t)=12 (for which the reaction rate is a maximum)
2006-07-20 12:36:37 · answer #4 · answered by Alice Lou 2 · 0⤊ 0⤋
I couldn't even find the concentration to get through reading the question!
2006-07-20 06:22:17 · answer #5 · answered by Anonymous · 0⤊ 0⤋
hah a i dont know if annyone could solve that in here
2006-07-20 06:20:51 · answer #6 · answered by mandy_2289 2 · 0⤊ 0⤋
I'd go with (d) all of the above
2006-07-20 06:18:55 · answer #7 · answered by JonJon McClaine 2 · 0⤊ 0⤋
good luck with that it sounds like you need it
2006-07-20 06:24:45 · answer #8 · answered by Randomness 2 · 0⤊ 0⤋
i don't even wanna try. sorry. i just read a bit and.. yeah.. sorry.
2006-07-20 06:18:17 · answer #9 · answered by ..:::Candy:::.. 1 · 0⤊ 0⤋
soorry friend
2006-07-20 06:19:28 · answer #10 · answered by Dr. Rahumika 2 · 0⤊ 0⤋