The count in a bacteria culture was 300 after 10 minutes and 1400 after 30 minutes.

The count in a bacteria culture was 300 after 10 minutes and 1400 after 30 minutes.

a) What was the initial size of the culture?

b) Find the doubling period.

c) Find the population after 60 minutes.

d) When will the population reach 12000

thank you!!

General expression,
P = 300 (1400/300)^[(t-10)/20]
a) P(0) ~ 139
b) Solve 2 = (1400/300)^(t/20) for t,
t ~ 9 min
c) P(60) ~ 14,114
d) Solve 12000 = 300 (1400/300)^[(t-10)/20] for t,
t = 57.89 min
So, after 57.89 min, the population reaches 12000.

1400=300e^(20k)
20k=ln(14/3)
k=[ln(14/3)]/20
k=0.077022
a)
300=Qoe^10k Qo=initial size of the culture
Qo=300/e^10k
Qo=139
b)
2=e^tk
tk=ln(2)
t=ln(2)/k
t=8.9993 min
c)
Q(60)=Qoe^60k
=14,136
d)
12000=Qoe^kt
kt=ln(12,000/Qo)
t=ln(12,000/Qo)/k
t=57.894 min
t=57 min 53.6 sec