The number of bacteria in a certain culture is initially 750

The number of bacteria in a certain culture is initially 750, and the culture doubles in size every day.

(a) Find the number of bacteria present after one day, two days, and three days.

(b) Find a formula for the number of bacteria present after n days.

Solution

Intial amt. Ao = 750

Doubles in size every day

Let the growth model be given as: A(t) = Aoe^kt

2Ao = A0 e^(k*1)

2 = e^k

k = ln2 =0.693

A(n) = 750e^0.693n ; n is no. of days

a)

after 1 day ; A = 750e^(1*0.693) = 750*2 = 1500 bacterias

after 2day ; A = 750e^(2*0.693) = 750*4 = 3000 bacterias

after 3 days ; A = 750e^(3*0.693) = 750*6 = 4500 bacterias

b) A(n) = 750e^(0.693n) ; n is no. of days