tomynator123456
New member
- Joined
- Nov 30, 2021
- Messages
- 7
Hello dear forum, I have been thinking a while over a problem in my studies which is a math problem.
Lets say we have a bacterium B that multiplies itself according to the exponential growth equation: B(t)=B(0)*e^(kt). B(t) is the number of bacteria B at the time point t, B(0) is the number of B at the time point 0, k is the growth rate in 1/h and t the time in h.
The bacterium B is able to produce a protein P at the rate p in 1/s, but when it does so, the growth rate k drops to a lower growth rate h. How can one calculate what the optimal time point d in hours for the start of the protein P production is?
Lets say that:
B(0)=1
k=1/h
t=24h (the total time that is available
P(0)=0
p=1/s=3600/h
h=0.5/h
So the point is to find the optimal trade off between maximum number of production units B that are present, because each B produces one P per second. On the other hand, if we wait longer than there is less time for all the present B to produce P.
And when the B start to produce P they still grow, only slower compared when they produce no P, so if P production starts it will increase over time because the number of producing units B still increases.
I am grateful for every help!
Greetings,
Thomas
Lets say we have a bacterium B that multiplies itself according to the exponential growth equation: B(t)=B(0)*e^(kt). B(t) is the number of bacteria B at the time point t, B(0) is the number of B at the time point 0, k is the growth rate in 1/h and t the time in h.
The bacterium B is able to produce a protein P at the rate p in 1/s, but when it does so, the growth rate k drops to a lower growth rate h. How can one calculate what the optimal time point d in hours for the start of the protein P production is?
Lets say that:
B(0)=1
k=1/h
t=24h (the total time that is available
P(0)=0
p=1/s=3600/h
h=0.5/h
So the point is to find the optimal trade off between maximum number of production units B that are present, because each B produces one P per second. On the other hand, if we wait longer than there is less time for all the present B to produce P.
And when the B start to produce P they still grow, only slower compared when they produce no P, so if P production starts it will increase over time because the number of producing units B still increases.
I am grateful for every help!
Greetings,
Thomas