Question

The number of bacteria at the beginning of an experiment was 30 and the bacteria grow at an hourly rate of 1.4 percent. Using the model given by () = 0e, estimate the number of bacteria, rounded to the nearest whole number after 20 hours.

Answer 1

Answer:

The estimated number of bacteria after 20 hours is 40.

Step-by-step explanation:

This is a case where a geometrical progression is reported, which is a particular case of exponential growth and is defined by the following formula:

$n(t) = n_{o}\cdot \left(1+\frac{r}{100} \right)^{t}$ (1)

Where:

$n_{o}$ - Initial number of bacteria, dimensionless.

$r$ - Increase growth of the experiment, expressed in percentage.

$t$ - Time, measured in hours.

$n(t)$ - Current number of bacteria, dimensionless.

If we know that $n_{o} = 30$, $r = 1.4$ and $t = 20\,h$, then the number of bacteria after 20 hours is:

$n(t) = 30\cdot \left(1+\frac{1.4}{100} \right)^{20}$

$n(t) \approx 39.616$

$n(t) = 40$

The estimated number of bacteria after 20 hours is 40.