A culture of bacteria has an initial population of 96000 bacteria and
doubles every 4 hours. Using the formula , where is the
population after thours, is the initial population, is the time in
hours and d is the doubling time, what is the population of bacteria in the
culture atter 11 hours, to the nearest whole number?

Ask by Vargas Pollard. in the United States

Mar 21,2025

Question

A culture of bacteria has an initial population of 96000 bacteria and
doubles every 4 hours. Using the formula , where is the
population after thours, is the initial population, is the time in
hours and d is the doubling time, what is the population of bacteria in the
culture atter 11 hours, to the nearest whole number?

Ask by Vargas Pollard. in the United States

Mar 21,2025

UpStudy AI · Accepted Answer

To find the population of bacteria in the culture after 11 hours, we can use the formula provided:

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

Given:
- Initial population $$ P_{0} = 96000 $$ bacteria
- Doubling time $$ d = 4 $$ hours
- Time $$ t = 11 $$ hours

Substitute the given values into the formula:

$$ P_{11} = 96000 \cdot 2^{\frac{11}{4}} $$

Now, we can calculate the population of bacteria after 11 hours using the formula.
Calculate the value by following steps:
- step0: Calculate:
  $$96000\times 2^{\frac{11}{4}}$$
- step1: Rewrite the expression:
  $$96000\times 4\sqrt[4]{2^{3}}$$
- step2: Calculate:
  $$96000\times 4\sqrt[4]{8}$$
- step3: Calculate:
  $$384000\sqrt[4]{8}$$
The population of bacteria in the culture after 11 hours is approximately 645808 bacteria, to the nearest whole number.
The population of bacteria after 11 hours is approximately 645,808.

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