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A certain type of bacteria decreases its population after exposure to a new antibiotic according to the model f(x) = 12.6(0.91)*, where the units of x are hours and the units of f(x) are thousands. What is the population of the bacteria in thousands after 5 hours? Round your answer to the nearest tenth of a thousand. Do not use spaces or commas in your answer. For example, if the answer is 46.3765thousand then enter your answer as: 46.4

Respuesta :

Given:

A certain type of bacteria decreases its population after exposure to a new antibiotic according to the model

[tex]f(x)=12.6(0.91)^x[/tex]

Required:

To find the population of the bacteria in thousands after 5 hours.

Explanation:

Consider

[tex]f(x)=12.6(0.91)^x[/tex]

When x = 5 hours,

[tex]\begin{gathered} f(x)=12.6(0.91)^5 \\ \\ =12.6(0.6240) \\ \\ =7.8628 \\ \\ \approx7.9 \end{gathered}[/tex]

Final Answer:

population of the bacteria is 7.9

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