Question

A bacteria culture doubles every 5 hours. Determine the hourly growth rate of the bacteria

Answer 1

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%.

A similar problem is given at brainly.com/question/24218305

Answer 2

Answer:

10

Step-by-step explanation: