A culture of bacteria has an initial population of 57000 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 8 hours, to the nearest whole number?

Ask by Warner Whittaker. in the United States

Mar 21,2025

Question

A culture of bacteria has an initial population of 57000 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 8 hours, to the nearest whole number?

Ask by Warner Whittaker. in the United States

Mar 21,2025

UpStudy AI · Accepted Answer

To find the population of bacteria in the culture after 8 hours, we can use the formula provided:

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

Given:
- Initial population $$ P_{0} = 57000 $$ bacteria
- Doubling time $$ d = 9 $$ hours
- Time $$ t = 8 $$ hours

Substitute the given values into the formula:

$$ P_{8} = 57000 \cdot 2^{\frac{8}{9}} $$

Now, we can calculate the population of bacteria after 8 hours using the formula.
Calculate the value by following steps:
- step0: Calculate:
  $$57000\times 2^{\frac{8}{9}}$$
- step1: Rewrite the expression:
  $$57000\sqrt[9]{2^{8}}$$
- step2: Calculate:
  $$57000\sqrt[9]{256}$$
The population of bacteria in the culture after 8 hours is approximately 105549.717201. Rounding this to the nearest whole number, the population after 8 hours is approximately 105550 bacteria.
After 8 hours, the population of bacteria is approximately 105,550.

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