Answer:
The approximate population of bacteria in the culture after 10 hours is 93,738.
Step-by-step explanation:
<h3>
General Concepts:</h3>
- Exponential Functions.
- Exponential Growth.
- Doubling Time Model.
- Logarithmic Form.
BPEMDAS Order of Operations:
- Brackets.
- Parenthesis.
- Exponents.
- Multiplication.
- Division.
- Addition.
- Subtraction.
<h2>Definitions:</h2>
We are given the following Exponential Growth Function (Doubling Time Model), where:
- The population of bacteria after “<em>t </em>” number of hours.
- The initial population of bacteria.
- Time unit (in hours).
- Doubling time, which represents the amount of time it takes for the population of bacteria to grow exponentially to become twice its initial quantity.
<h2>Solution:</h2>
<u>Step 1: Identify the given values.</u>
- 9,300.
- <em>t</em> = 10 hours.
- <em>d</em> = 3.
<u>Step 2: Find value.</u>
1. Substitute the values into the given exponential function.
2. Evaluate using the BPEMDAS order of operations.
Hence, the population of bacteria in the culture after 10 hours is approximately 93,738.
<h2>Double-check:</h2>
We can solve for the amount of <u>time</u> <u>(</u><em>t</em> ) it takes for the population of bacteria to increase to 93,738.
1. Identify given:
- .
- .
- <em>d </em>= 3.
2. Substitute the values into the given exponential function.
3. Divide both sides by 9,300:
4. Transform the right-hand side of the equation into logarithmic form.
5. Take the <em>log</em> of both sides of the equation (without rounding off any digits).
6. Divide both sides by (0.301029996).
7. Multiply both sides of the equation by 3 to isolate "<em>t</em>."
Hence, it will take about 10 hours for the population of bacteria to increase to 93,378.
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Learn more about Exponential Functions on:
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