Mathematics: A bacteria culture doubles every 5 hours. Determine the hourly growth rate of the bacteria culture. Round your answer to the nearest tenth of a percent.

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A bacteria culture doubles every 5 hours. Determine

IntellTanito

27.09.2021

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:

A(t) = A(0)(1+r)^t

In which:

A(0) is the initial amount.r is the hourly growth rate.

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Since it doubles every 5 hours, it means that:

A(5) = 2A(0)

And we use this to find r.

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A(t) = A(0)(1+r)^t

2A(0) = A(0)(1+r)^5

(1 + r)^5 = 2

$\sqrt[5]{(1 + r)^5} = \sqrt[5]{2}$

$1 + r = 2^{\frac{1}{5}}$

1 + r = 1.149

r = 1.149 - 1 = 0.149

0.149*100% = 14.9%.

The hourly growth rate of the bacteria culture is of 14.9%.

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