A culture of bacteria has an initial population of 4800 bacteria and
doubles every 9 hours. Using the formula , where is the
population after hours, is the initial population, is the time in
hours and is the doubling time, what is the population of bacteria in the
culture after 14 hours, to the nearest whole number?

Ask by Alexander Garrett. in the United States

Mar 21,2025

Question

A culture of bacteria has an initial population of 4800 bacteria and
doubles every 9 hours. Using the formula , where is the
population after hours, is the initial population, is the time in
hours and is the doubling time, what is the population of bacteria in the
culture after 14 hours, to the nearest whole number?

Ask by Alexander Garrett. in the United States

Mar 21,2025

UpStudy AI · Accepted Answer

To find the population of bacteria in the culture after 14 hours, we can use the formula provided:

$$ P_{t} = P_{0} \cdot 2^{\frac{t}{d}} $$

Given:
- Initial population $$ P_{0} = 4800 $$ bacteria
- Doubling time $$ d = 9 $$ hours
- Time $$ t = 14 $$ hours

Substitute the given values into the formula:

$$ P_{14} = 4800 \cdot 2^{\frac{14}{9}} $$

Now, we can calculate the population of bacteria after 14 hours using the formula.
Calculate the value by following steps:
- step0: Calculate:
  $$4800\times 2^{\frac{14}{9}}$$
- step1: Rewrite the expression:
  $$4800\times 2\sqrt[9]{2^{5}}$$
- step2: Calculate:
  $$4800\times 2\sqrt[9]{32}$$
- step3: Calculate:
  $$9600\sqrt[9]{32}$$
The population of bacteria in the culture after 14 hours is approximately 14109.451126. Rounding this to the nearest whole number, the population of bacteria in the culture after 14 hours is approximately 14109 bacteria.
After 14 hours, there are approximately 14,109 bacteria in the culture.

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