Question

If 7,200 bacteria, with a growth constant k=1.8 per hour, are present at the beginning of the experiment, in how many hours will there be 15,000 bacteria?

Answer 1

here's an example

Explanation:

Given:

Initial number of bacteria = 3000

With a growth constant (k) of 2.8 per hour.

To find:

The number of hours it will take to be 15,000 bacteria.

Solution:

Let P(t) be the number of bacteria after t number of hours.

P(t)=poe

The exponential growth model (continuously) is:

Where, p0 is the initial value, k is the growth constant and t is the number of years.

Putting P(t)=15000,P0=3000,k=2.8 on the above formula we get

15000=3000e2.8

15000

----------- = e2.8

3000

5=e2.8

Taking ln on both sides, we get

in 5= in e2.8

1.609438=2.8

1.609438

________ =t

2.8

0.574799=t

t= 0.575

Therefore, the number of bacteria will be 15,000 after 0.575 hours.