Question

Time (hours) Number of Cells

0 200
.25 400
.5 800
.75 1600
1 3200

Write the rule of the function that gives the number of C cells at time t hours.
C(t) =
...?

Answer 1

I was thinking here of using the Monod Kinetics equation, however it seems that the given is lacking. So we will just use a first order growth kinetics since this is more commonly used. The derived first order kinetics for cell growth is

C = Co * e^(kt)

where

C = number of cells at any time
Co = initial number of cells
k = is the growth constant
t = time

in this case, Co is the number of cells at time t=0. The growth constant k is unknown. This can be obtained from the data given. We need to linearize the first order equation that is,

ln C = ln Co + kt

using the calculator or MS excel, obtain the slope (k) by plotting the ln (C) vs t. After doint that we can obtaine a k of 2.77 and therfore the equation is

C = 200*e^(2.77t)