Question

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

Answer 1

Answer:

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

Step-by-step 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 ,

$240 = 120 e^{30k}$

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

$ln(\frac{240}{120}) = 30 k$

ln(2) = 30 k

0.693  = 30k

$k = \frac{0.693}{30}$

k = 0.023

Now the equation  for the bacteria at x hours is

$N(x) = N_0e^{0.023x}$