The number of bacteria in a Petri dish was initially determined to be 1. After one hour, the number of bacteria had increased to 3 and after another hour to 6. Assume that the rate of growth of bacteria in the dish at any time t can be calculated using the logistic equation

dB/dt =B(a-bB)

(a) Determine the number of bacteria in the dish after an additional hour has passed.

(b) Determine the carrying capacity of the dish based on the developed logistic equation.

a) the number of bacteria in the dish after an additional hour has passed = 8

b) the carrying capacity of the dish based on the developed logistic equation. = 9

Step-by-step explanation:

Given that ;

The Logistic growth model is :

Solving the above equation  ; we have a MODEL EQUATION;

in which:

represents the initial population of the bateria.

We are given that the number of the bacteria in the Petri dish was initially determined to be 1 , then ;

After an hour ; we were told that the number of the bacteria increased to 3 ; So:

Similarly after (2) hours; the number of the bacteria increased to 6; then

So;

Solving for a and b from the above two eqautions: Then,

a = 1.386

b =  0.154

Substituting the value of a and b  into our MODEL EQUATION; we have

a)  Determine the number of bacteria in the dish after an additional hour has passed.

i.e at t = 3

b) Determine the carrying capacity of the dish based on the developed logistic equation.

The carrying capacity B can be expressed as :

B =9

1 ans is 49

as its root is 7 and double of 7 id 14

2 ans is

sq of 64 is 8

number is x

now

5x + 4 = 64

5x=60

x=12

so number is 12.