Math Problem Statement
Solution
The question asks which of the contexts represents exponential growth. Let's analyze each of the options:
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The amount of certain medication in a person's bloodstream decreases by every hour.
- This represents exponential decay (not growth), as the amount of medication is decreasing over time.
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A population of 200 bacteria quintuples every week.
- This is an example of exponential growth because the population increases by a factor of 5 every week, which is a characteristic of exponential growth.
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Snow was falling at a rate of 1.75 inches per hour.
- This describes linear growth, not exponential growth, because the snow falls at a constant rate.
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A car depreciates at a rate of 5.3% per year.
- This is exponential decay, as the car's value decreases by a fixed percentage each year.
So, the correct context representing exponential growth is "A population of 200 bacteria quintuples every week."
Would you like a more detailed explanation or have any further questions?
Here are five related questions for further exploration:
- How do we define exponential growth in mathematical terms?
- Can exponential growth ever slow down over time?
- What are some real-life examples of exponential growth?
- How do you calculate exponential growth using a formula?
- What is the difference between exponential growth and linear growth?
Tip: To identify exponential growth, look for situations where the quantity is multiplying by a fixed factor over time.
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Math Problem Analysis
Mathematical Concepts
Exponential Growth
Exponential Decay
Linear Growth
Formulas
Exponential Growth Formula: P(t) = P_0 * r^t
Theorems
Properties of Exponential Functions
Suitable Grade Level
Grades 8-10