Question

The number of bacteria in a certain population increases according to a continuous exponential growth model, with a growth rate parameter of 5.3% per hour. How many hours does it take for the size of the sample to double?

Answer 1

Answer:

The size of sample to double after 13.08 hours.

Step-by-step explanation:

Formula of exponential growth

$A=A_0e^{rt}$

A=The number of bacteria after t time.

$A_0$ = The number of bacteria when t=0.

r= rate of growth

t= time.

The size of the sample will be double.

It means ,

$A=2 A_0$, r= 5.3%=0.053

$A=A_0e^{rt}$

$\Rightarrow 2 A_0=A_0e^{0.053t}$

$\Rightarrow 2 =e^{0.053t}$

Taking ln both sides

$\Rightarrow ln(2) =ln(e^{0.053t})$

$\Rightarrow ln (2)= 0.053t$

$\Rightarrow t=\frac{ ln (2)}{ 0.053}$

⇒t=13.08 h

The size of sample to double after 13.08 hours.