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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

User Csislander
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1 Answer

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Answer:

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

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.

User Lakshya Thakur
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