suppose that the number of bacteria in a certain population increases according to a continuous exponential growth model, with a growth rate parameter of per hour. suppose also that a sample culture of bacteria is obtained from this population. find the size of the sample after two hours. round your answer to the nearest integer.

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09-12-2022
Mathematics

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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 per hour. suppose also that a sample culture of bacteria is obtained from this population. find the size of the sample after two hours. round your answer to the nearest integer.

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qwcherry qwcherry · Answer 1 · 2022-12-17T12:45:06-05:00

The size of the sample after two hours with an initial population of 1000 and a growth rate of 11% is found to be 1246.

A pattern of data that exhibits larger increases over time, forming the curve of an exponential function, is said to exhibit exponential growth. The formula of continuous exponential growth is P=P₀e^{rt} where P is the population after time t, P₀ is the initial population, and r is the growth rate.

Given P₀ is 1000 bacteria, r is 11% = 0.11, and t is 2 hours. Then, the size of the sample after two hours is,

[tex]\begin{aligned}P&=P_0e^{rt}\\&=1000e^{0.11\times2}\\&=1000e^{0.22}\\&=1000\times1.246\\&=1246\end{aligned}[/tex]

The answer is 1246.

The complete question is -

Suppose that the number of bacteria in a certain population increases according to a continuous exponential growth model, with a growth rate parameter of 11% per hour. Suppose also that a sample culture of 1000 bacteria is obtained from this population. Find the size of the sample after two hours. Round your answer to the nearest integer.

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