One year, Mr James travels 9 x 10^3 miles for his job. The next year he traveled 1 x 10^4 miles. How many more miles did he trav
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Answer:
- <u>Question 1:</u>
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- <u>Question 2:</u>
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- <u>Question 3:</u>
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- <u>Question 4:</u>
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Explanation:
<u>Question 1: Write down the differential equation the mass of the bacteria, m, satisfies: m′= .2m</u>
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a) By definition:
b) Given:
c) By substitution:
<u>Question 2: Find the general solution of this equation. Use A as a constant of integration.</u>
a) <u>Separate variables</u>
b)<u> Integrate</u>
c) <u>Antilogarithm</u>
<u>Question 3. Which particular solution matches the additional information?</u>
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Use the measured rate of 4 grams per hour after 3 hours
First, find the mass at t = 3 hours
Now substitute in the general solution of the differential equation, to find A:
Round A to 1 significant figure:
- A = 10.
<u>Particular solution:</u>
<u>Question 4. What was the mass of the bacteria at time =0?</u>
Substitute t = 0 in the equation of the particular solution: