Using an exponential function, it is found that the hourly growth rate of the bacteria culture is of 14.9%.
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An exponential function has the following format:
[tex]A(t) = A(0)(1+r)^t[/tex]
In which:
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Since it doubles every 5 hours, it means that:
[tex]A(5) = 2A(0)[/tex]
And we use this to find r.
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[tex]A(t) = A(0)(1+r)^t[/tex]
[tex]2A(0) = A(0)(1+r)^5[/tex]
[tex](1 + r)^5 = 2[/tex]
[tex]\sqrt[5]{(1 + r)^5} = \sqrt[5]{2}[/tex]
[tex]1 + r = 2^{\frac{1}{5}}[/tex]
[tex]1 + r = 1.149[/tex]
[tex]r = 1.149 - 1 = 0.149[/tex]
0.149*100% = 14.9%.
The hourly growth rate of the bacteria culture is of 14.9%.
A similar problem is given at https://brainly.com/question/24218305
