Question

120 bacteria in a Petri dish double every 30 minutes. Write an equation for the amount of bacteria after x hours.

Answer 1

`N(x) = N_0e^(0.023x)` is the equation for the amount of bacteria after x hours.

Explanation:

Given:

Number of Bacteria in perti dish = 120

The time taken for the bacteria to double = 30 minutes

To Find:

The equation for the amount of bacteria after x hours = ?

Solution:

The exponential growth formula is

`N(t) = N_0e^(kt)`

where

N(t) is the amount of bacteria at time t

k is the growth rate

`N_0` is the initial number of bacteria

we know that at t=30 min N(30) = 2*120 ,

`240 = 120 e^(30k)`

`ln ( 240) = ln (120) \cdot{30 k}`

`ln((240)/(120)) = 30 k`

ln(2) = 30 k

0.693 = 30k

`k = (0.693)/(30)`

k = 0.023

Now the equation for the bacteria at x hours is

`N(x) = N_0e^(0.023x)`