Question

A certain cell culture grows at a rate proportional to the number of cells
present. If the culture contains 500 cells initially and 800 after 24 hours, how
many cells will be present after a further 12 hours?

Answer 1

let x = number of cells at time t
dx/dt = kx
solving this differential equation gives

x =500 e^(kt)

when x = 800, t = 1 (day):
800 = 500e^k
k = 0.47
so x = 500e^(0.47t)


so after another 12 hours when t = 1.5

x = 500e^(0.47*1.5)
x = 1012

Answer 2

1012