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.

Question

asked Nov 21, 2022 166k views

1 Answer

Vineeth Mohan · Answer 1 · 2022-11-24T17:09:52+0000

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