Question

Suppose that the number of bacteria in a certain population increases according to a continuous exponential growth model, with a growth rate parameter of 17% per hour. Suppose also that a sample culture of 1600 is obtained from this population. Find the size of the sample after four hours. Round your awnser to the nearest integer

Answer 1

Answer:

The size of the sample after four hours is of 3158 bacteria.

Step-by-step explanation:

The population after t hours can be modeled by the continuous exponential growth model, which is:

$P(t) = P(0)e^{rt}$

In which P(0) is the initial population and r is the growth rate paremeter.

A growth rate parameter of 17% per hour.

This means that $r = 0.17$

Suppose also that a sample culture of 1600 is obtained from this population.

This means that $P(0) = 1600$

Find the size of the sample after four hours.

This is P(4).

$P(t) = P(0)e^{rt}$

$P(t) = 1600e^{0.17t}$

$P(4) = 1600e^{0.17*4}$

$P(4) = 3158.2$

Rounding to the nearest integer

The size of the sample after four hours is of 3158 bacteria.