Question

The rate of increase of the bacteria in a certain culture is proportional to the number present.It is doubles in 5 hours then in 25, hours, its number would be

Answer 1

Answer:

Step-by-step explanation:

We take this as an exponential growth.

The formula is thus :

N(t) = Noe^kt

Where :

N(t) is the population at time t.

No = initial population

k = rate of increase.

t = time

Let us take the initial population of the bacteria to be 1.

t = 5

N(t) = 2

We are looking for k.

Doing the substitution we have :

2 = e^5k

ln 2 = 5k

0.69315 = 5k

k = 0.69315/5

k = 0.13863

In 25 hours time the population will be :

N(25) = e^(0.13863 × 25)

= e^3.46575

= 32.000

The bacteria will be 32 times the original population.