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stepan [7]
2 years ago
14

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

Mathematics
1 answer:
Gennadij [26K]2 years ago
5 0

\sqrt[5]{2}-1 = 1 +x - 1Answer:

14.87% per hour

Step-by-step explanation:

Let's pretend we're starting with one bacteria.

Double of one is two

We're gonna have to use this formula: A = P(1 + x)ⁿ

A = Amount (which is 2)

P = Initial amount (which is 1)

x = percentage per time (hour)

n = amount of time (hours)

So our equation will look like this:

2 = 1(1 + x)⁵

First, we need to root both sides to isolate (1 + x)

\sqrt[5]{2} = \sqrt[5]{(1+x)}

\sqrt[5]{2} = 1 +x

Then subtract both sides by 1

\sqrt[5]{2}-1 = 1 +x - 1

x=\sqrt[5]{2}-1

\sqrt[5]{2} = 1.148698355

1.148698355 - 1 = 0.148698355

x = 0.148698355

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\large\underline{\sf{Solution-}}

<h2 /><h2><u>Consider</u></h2>

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<h2><u>W</u><u>e</u><u> </u><u>K</u><u>n</u><u>o</u><u>w</u><u>,</u></h2>

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\boxed{\tt{ \cos \bigg( \frac{3\pi}{2} + x \bigg) \cos \: (2\pi + x) \bigg \{ \cot \bigg( \frac{3\pi}{2} - x \bigg) + cot(2\pi + x) \bigg \} = 1}}

▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬

<h2>ADDITIONAL INFORMATION :-</h2>

Sign of Trigonometric ratios in Quadrants

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