Question

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.

Answer 1

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

14.87% per hour

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