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d. The amount of bacteria after n min if the initial amount of bacteria is q and the amount of bacteria triples every 20 sec. (Hint: The answer should contain q as well as n) The expression for the amount of bacteria is

d. The amount of bacteria after n min if the initial amount of bacteria is q and the amount of bacteria triples every 20 sec. (Hint: The answer should contain q as well as n) The expression for the amount of bacteria is

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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**Mathematical Problem Solving** d. **Bacteria Growth Over Time** - **Problem:** Calculate the amount of bacteria after \( n \) minutes if the initial amount of bacteria is \( q \) and the amount of bacteria triples every 20 seconds. *(Hint: The answer should contain \( q \) as well as \( n \)).* - **Expression:** The expression for the amount of bacteria is \(\boxed{}\). - **Instruction:** Simplify your answer. **Explanation:** To solve this, we recognize that 20 seconds is \(\frac{1}{3}\) of a minute. Therefore, the bacteria triple every \(\frac{1}{3}\) of a minute. If the time in minutes is \( n \), after each minute the bacteria would have tripled \((3 \times n)\) times, hence the expression for the amount of bacteria. e. **Temperature Drop Over Time** - **Problem:** Calculate the temperature \( t \) hours ago if the present temperature is \( 50^\circ F \) and it drops by \( 4^\circ F \) each hour. - **Expression:** The expression for the temperature is \(\boxed{}\) °F. - **Instruction:** Simplify your answer. **Explanation:** You need to subtract \( 4^\circ F \) multiplied by the number of hours ago (\( t \)) from the current temperature to find out how much the temperature was \( t \) hours ago. f. **Total Earnings Calculation** - **Problem:** Calculate Pawel's total earnings after 3 years if in the first year his salary was \( s \) dollars, in the second year it was $5000 higher, and in the third year it was twice as much as the first year. - **Expression:** The expression for Pawel's total earnings is \(\boxed{}\) dollars. - **Instruction:** Simplify your answer. **Explanation:** To solve this, calculate each year's salary: - First Year: \( s \) - Second Year: \( s + 5000 \) - Third Year: \( 2 \times s \) Then, sum these amounts to get the total earnings after 3 years. --- *This page provides key mathematical expressions to solve common scenarios through algebraic manipulation. Each section provides a problem statement and guides the user to formulating and simplifying the required expressions. For personalized educational support, feel free
Transcribed Image Text:**Mathematical Problem Solving** d. **Bacteria Growth Over Time** - **Problem:** Calculate the amount of bacteria after \( n \) minutes if the initial amount of bacteria is \( q \) and the amount of bacteria triples every 20 seconds. *(Hint: The answer should contain \( q \) as well as \( n \)).* - **Expression:** The expression for the amount of bacteria is \(\boxed{}\). - **Instruction:** Simplify your answer. **Explanation:** To solve this, we recognize that 20 seconds is \(\frac{1}{3}\) of a minute. Therefore, the bacteria triple every \(\frac{1}{3}\) of a minute. If the time in minutes is \( n \), after each minute the bacteria would have tripled \((3 \times n)\) times, hence the expression for the amount of bacteria. e. **Temperature Drop Over Time** - **Problem:** Calculate the temperature \( t \) hours ago if the present temperature is \( 50^\circ F \) and it drops by \( 4^\circ F \) each hour. - **Expression:** The expression for the temperature is \(\boxed{}\) °F. - **Instruction:** Simplify your answer. **Explanation:** You need to subtract \( 4^\circ F \) multiplied by the number of hours ago (\( t \)) from the current temperature to find out how much the temperature was \( t \) hours ago. f. **Total Earnings Calculation** - **Problem:** Calculate Pawel's total earnings after 3 years if in the first year his salary was \( s \) dollars, in the second year it was $5000 higher, and in the third year it was twice as much as the first year. - **Expression:** The expression for Pawel's total earnings is \(\boxed{}\) dollars. - **Instruction:** Simplify your answer. **Explanation:** To solve this, calculate each year's salary: - First Year: \( s \) - Second Year: \( s + 5000 \) - Third Year: \( 2 \times s \) Then, sum these amounts to get the total earnings after 3 years. --- *This page provides key mathematical expressions to solve common scenarios through algebraic manipulation. Each section provides a problem statement and guides the user to formulating and simplifying the required expressions. For personalized educational support, feel free
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