The count in a bateria culture was 600 after 15 minutes and

The count in a bateria culture was 600 after 15 minutes and 1600 after 40 minutes. Assuming the count grows exponentially,

What was the initial size of the culture?     

Find the doubling period.     

Find the population after 95 minutes.     

When will the population reach 14000

Solution

Let the growth equation be : N(t) = Noe^kt

600 after 15 minutes and 1600 after 40 minutes

Use these points to establish the equation :

600 = Noe^15k ----(1)

1600 = Noe^40k -----(2)

Divide equation 2 by 1:

16/6 = e^25k

Take natural log on both sides:

ln(16/6) = 25k ; k = 0.039

So, N(t) = Noe^0.039t

600 = Noe^(0.039*15)

600/e^0.585 = No

No = 335 (Intial size of culture)

Doubling period : T1/2 = 0.693/0.039 = 17.77 minutes

Aftet 95 min. : N(95) = 335e^(0.039*95) = 335e^3.705

= 335*40.65 = 13617.75

When will the population reach 14000 ?

14000 = 335e^(0.035t)

t = 106.65 minutes