A culture of bacteria has an initial population of 3900 bacteria and
doubles every 2 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 9 hours, to the nearest whole number?

Ask by Donnelly Cummings. in the United States

Mar 21,2025

Question

A culture of bacteria has an initial population of 3900 bacteria and
doubles every 2 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 9 hours, to the nearest whole number?

Ask by Donnelly Cummings. in the United States

Mar 21,2025

UpStudy AI · Accepted Answer

To find the population of bacteria in the culture after 9 hours, we can use the formula provided:

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

Given:
- Initial population $$ P_{0} = 3900 $$ bacteria
- Doubling time $$ d = 2 $$ hours
- Time $$ t = 9 $$ hours

Substitute the given values into the formula:

$$ P_{9} = 3900 \cdot 2^{\frac{9}{2}} $$

Now, we can calculate the population of bacteria after 9 hours using the formula.
Calculate the value by following steps:
- step0: Calculate:
  $$3900\times 2^{\frac{9}{2}}$$
- step1: Rewrite the expression:
  $$3900\times 16\sqrt{2}$$
- step2: Expand the expression:
  $$62400\sqrt{2}$$
The population of bacteria in the culture after 9 hours is approximately 88247 bacteria, to the nearest whole number.
After 9 hours, the population of bacteria is approximately 88,247.

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