If in culture of yeast the rate of growth y'(t) is proportional to the amount y(t ) present at time t, and if y(t) doubles in 1 day, how much can be expected after 3 days at the same rate of the growth? After 1 week

Question

 
 (Hint: Continuous growth model)
 

Answer 1

Since we are "doubling" it is easy to use a base of 2
amount = a(2)^(t/1)
= a (2)^t , where t ≥ 0, and t=0 ---> now

after 1 day we have 2a
after 3 days , we have a(2)^3 or 8a
after 1 week , we have a(2)^7 = 128a

normally we would use base e
here we have
amount = a e^(kt), where k is a constant
so after 1 day:
2a = a e^k
2 = e^k
k = ln2

amount = a e^(ln2 t)
checking with our previous answer:
if t = 7
amount = a e(7ln2) = 128a